ORIGINAL_ARTICLE
On generalized topological molecular lattices
In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices, topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and define a closed element by the pseudocomplement of an open element. We have two structures on a completely distributive complete lattice, topology and generalized co-topology which are not dual to each other. We study the basic concepts, in particular separation axioms and some relations among them.
https://scma.maragheh.ac.ir/article_27148_12786ed7e1649bbde8c31adf30c4807c.pdf
2018-04-01
1
15
10.22130/scma.2017.27148
Topological molecular lattice
Generalized Topological molecular lattice
Generalized order homomorphism
Separation axiom
Narges
Nazari
nazarinargesmath@yahoo.com
1
Department of Mathematics, University of Hormozgan, Bandarabbas, Iran.
AUTHOR
Ghasem
Mirhosseinkhani
gh.mirhosseini@yahoo.com
2
Department of Mathematics, Sirjan University of Technology, Sirjan, Iran.
LEAD_AUTHOR
[1] A.R. Aliabadi and A. Sheykhmiri, LG-topology, Bull. Iranian Math. Soc., 41 (2015), pp. 239-258.
1
[2] T.S. Blyth, Lattice and Ordered Algebraic Structures, Springer-Verlag, London, 2005.
2
[3] G. Bruns, Darstellungen und Erweiterungen geordneter Mengen II, J. Reine Angew. Math., 210 (1962), pp. 1-23.
3
[4] K. El-Saady and F. Al-Nabbat, Generalized topological molecular lattices, Advances in Pure Mathematics, 5 (2015), pp. 552-559.
4
[5] P.T. Johnstone, Stone spaces, Cambridge studies in Advanced Mathematics, Cambridge University press, cambridge, 1982.
5
[6] Y.M. Li, Exponentiable objects in the category of topological molecular lattices, Fuzzy sets and systems, 104 (1999), pp. 407-414.
6
[7] J. Picado and A. Pultr, Frames and locales, Topology Without Points, Frontiers in Mathematics, Birkhauser-Springer AG, Basel, 2012.
7
[8] S. Roman, Lattice and ordered sets, Springer, New York, 2008.
8
[9] W.J. Thron, Lattice-equivalence of topological spaces, Duke Math. J., 29 (1962), pp. 671-679.
9
[10] G.J. Wang, Theory of topological molecular lattices, Fuzzy Sets and Systems, 47 (1992), pp. 351-376.
10
[12] G.J. Wang, Generalized topological molecular lattices, Scientia Sinica, 8 (1984), pp. 785-798.
11
ORIGINAL_ARTICLE
Similar generalized frames
Generalized frames are an extension of frames in Hilbert spaces and Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an orthogonal projection. Moreover, a $g$-frame is obtained by two the $g$-frames and its operator duals are investigated. Finally, the dilation of $g$-frames is studied.
https://scma.maragheh.ac.ir/article_24628_6e243f25a60fbae52edb2214bfc74bcd.pdf
2018-04-01
17
28
10.22130/scma.2017.24628
Dual frame
Similar $g$-frames
Frame operator
$g$-frame
Operator dual frame
Azadeh
Alijani
a.alijani57@gmail.com
1
Department of Mathematics, Faculty of Science, Vali-e-Asr University of Rafsanjan, P.O. Box 7719758457, Rafsanjan, Iran.
LEAD_AUTHOR
[1] A. Alijani, Generalized frames with C*-valued bounds and their operator duals, Filomat, 29 (2015), pp. 1469-1479.
1
[2] A. Alijani and M.A. Dehghan, $G$-frames and their duals for Hilbert C*-modules, Bull. Iranian Math. Soc., 38 (2012), pp. 567-580.
2
[3] P.G. Casazza, The art of frame theory, Taiw. J. Math., 4 (2000), pp. 129-201.
3
[4] P.G. Casazza and G. Kutyniok, Finite Frames: Theory and Applications, Brikhauser Basel, 2013.
4
[5] M.A. Dehghan and M.A. Hasankhani Fard, G-Dual frames in Hilbert spaces, U.P.B. Sci. Bull., Series A, 75 (2013), pp. 129-140.
5
[6] M. Frank and D.R. Larson, Frames in Hilbert C*-modules and C*-algebra, J. Operator theory, 48 (2002), pp. 273-314.
6
[7] D. Han, W. Jing, D. Larson, and R. Mohapatra, Riesz bases and their dual modular frames in Hilbert C*-modules, J. Math. Anal. Appl., 343 (2008), pp. 246-256.
7
[8] A. Khosravi and B. Khosravi, Fusion frames and $g$-frames in Hilbert C*-modules, Int. J. Wavelets Multiresolut. Inf. Process., 6 (2008), pp. 433-446.
8
[9] A. Khosravi and B. Khosravi, g-frames and modular Riesz bases in Hilbert C*-modules, Int. J. Wavelets Multiresolut. Inf. Process., 10 (2012), pp. 1-12.
9
[10] E.C. Lance, Hilbert C*-modules, A Toolkit for Operator Algebraists, University of Leeds, Cambridge University Press, 1995.
10
[11] A. Najati and A. Rahimi, Generalized frames in Hilbert spaces, Bull. Iran Math. Soc., 35 (2009), pp. 97-109.
11
[12] W. Sun, G-Frames and $g$-Riesz bases, J. Math. Anal. Appl., 322 (2006), pp. 437-452.
12
ORIGINAL_ARTICLE
On $L^*$-proximate order of meromorphic function
In this paper we introduce the notion of $L^{* }$-proximate order of meromorphic function and prove its existence.
https://scma.maragheh.ac.ir/article_23127_4ad4d5505216e8a188a642efa29d1569.pdf
2018-04-01
29
35
10.22130/scma.2016.23127
Meromorphic function
$L^*$-order
$L^*$- proximate order
Sanjib
Datta
sanjib_kr_datta@yahoo.co.in
1
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.
LEAD_AUTHOR
Tanmay
Biswas
tanmaybiswas_math@rediffmail.com
2
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.
AUTHOR
[1] I. Lahiri, Generalised proximate order of meromorphic functions, Mat. Vesnik, 41 (1989), pp. 9-16.
1
[2] S.M. Shah, On proximate orders of integral functions, Bull. Amer. Math. Soc., 52 (1984), pp. 326-328.
2
[3] S.K. Singh and G.P. Barker, Slowly changing functions and their applications, Indian J. Math., 19 (1977), pp. 1-6.
3
[4] D. Somasundaram and R. Thamizharasi, A note on the entire functions of L-bounded index and L-type, Indian J. Pure Appl. Math., 19 (1988), pp. 284-293.
4
[5] G. Valiron, Lectures on the general theory of integral functions, Chelsea Publishing Company, 1949.
5
ORIGINAL_ARTICLE
The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions
Let $$(Lv)(t)=\sum^{n} _{i,j=1} (-1)^{j} d_{j} \left( s^{2\alpha}(t) b_{ij}(t) \mu(t) d_{i}v(t)\right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(\Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estimate the resolvent of the operator $L$ on the one-dimensional space $ L_{2}(\Omega)$ using some analytic methods.
https://scma.maragheh.ac.ir/article_27152_70e08c9b43440114768339d1f55188af.pdf
2018-04-01
37
46
10.22130/scma.2017.27152
Resolvent
Distribution of eigenvalues
Non-selfadjoint differential operators
Leila
Nasiri
leilanasiri468@gmail.com
1
Department of Mathematics and computer science, Faculty of science, Lorestan University, Khorramabad, Iran.
AUTHOR
Ali
Sameripour
asameripour@yahoo.com
2
Department of Mathematics and computer science, Faculty of science, Lorestan University, Khorramabad, Iran.
LEAD_AUTHOR
[1] K.Kh. Boimatov, Asymptotics of the spectrum of non-selfadjoint systems of second-order differential operators, (Russian) Mat. Zametki, 51 (1992), pp. 8-16.
1
[2] K.Kh. Boimatov, Asymptotic behavior of the spectra of second-order non-selfadjoint systems of differential operators, Mat. Zametki., 51 (1992), pp. 8-16.
2
[3] K.Kh. Boimatov, On the distribution of the eigenvalues of differential operators which depend polynominally on a small parameter, Bull. Iranian Math. Soc., 19 (1993), pp. 13-26.
3
[4] K.Kh. Boimatov, The generalized Dirichlet problem associated with noncoercive bilinear forms, (Russian) Dokl. Akad. Nauk., 330, (1993), pp. 285-290.
4
[5] K.Kh. Boimatov and A.G. Kostyuchenko, Distribution of eigenvalues of second-order non-selfadjoint differential operators, (Russian) Vest. Moskov. Univ. Ser. I Mat. Mekh., 3 (1990), pp. 24-31.
5
[6] K.Kh. Boimatov and A.G. Kostyuchenko, The spectral asymptotics of non-selfadjoint elliptic systems of differential operators in bounded domains, (Russian) Mat. Sb., 181 (1990), pp. 1678-1693.
6
[7] M.G. Gadoev, Spectral asymptotics of non -selfadjoint degenerate elliptic operators with singular matrix coefficients on an integral, Ufa mathematical journal, 3 (2011), pp. 26-53.
7
[8] I.C. Gokhberg and M.G. Krein, Introduction to the Theory of linear non-selfadjoint operators in Hilbert space, Amer. Math. Soc., Providence, R. I., 1969.
8
[9] T. Kato, Perturbation Theory for Linear operators, Springer, New York, 1966.
9
[10] L. Nasiri and A. Sameripour, Notes on spectral featurs of degenerate non-selfadjoint differential operators on elliptic systems and l-dimensional Hilbert spaces, Math. Sci. Lett., 6 (2017).
10
[11] A. Sameripour and K. Seddigh, Distribution of eigenvalues of non-selfadjoint elliptic systems on the domain boundary, (Russian) Mat. Zametki, 61 (1997), pp. 463-467.
11
[12] A. Sameripour and K. Seddighi, On the spectral properties of generelized non-selfadjoint elliptic systems of differential operators degenerated on the boundary of domain, Bull. Iranian Math. Soc., 24 (1998), pp. 15-32.
12
[13] A.A. Shkalikov, Tauberian type theorems on the distribution of zeros of holomorphic functions, Mat. Sb., 123 (1984), pp. 317-347.
13
ORIGINAL_ARTICLE
Existence of three solutions for a class of quasilinear elliptic systems involving the $p(x)$-Laplace operator
The aim of this paper is to obtain three weak solutions for the Dirichlet quasilinear elliptic systems on a bonded domain. Our technical approach is based on the general three critical points theorem obtained by Ricceri.
https://scma.maragheh.ac.ir/article_27915_096934b4d663bf9097f8a976dbefed6b.pdf
2018-04-01
47
60
10.22130/scma.2017.27915
Variable exponent Sobolev space
p(x)-Laplacian
Three solutions
Dirichlet problem
Ali
Taghavi
taghavi@umz.ac.ir
1
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
AUTHOR
Ghasem
Alizadeh Afrouzi
afrouzi@umz.ac.ir
2
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
AUTHOR
Horieh
Ghorbani
h.ghorbani@stu.umz.ac.ir
3
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
LEAD_AUTHOR
[1] E. Acerbi and G. Mingione, Regularity results for stationary electro-rheological fluids, Arch. Ration. Mech. Anal., 156 (2001), pp. 121-140.
1
[2] X.L. Fan, J. Shen, and D. Zhao, Sobolev embedding theorems for spaces Wk,p(x)(Ω), J. Math. Anal. Appl., 262 (2001), pp. 749-760.
2
[3] X.L. Fan and D. Zhao, On the spaces Lp(x)(Ω) and W1,p(x)(Ω), J. Math. Anal. Appl., 263 (2001), pp. 424-446.
3
[4] X.L. Fan and Q.H. Zhang, Existence of solutions for p(x)-Laplacian Dirichlet problems, Nonlinear Anal., 52 (2003), pp. 1843-1852.
4
[5] A.El. Hamidi, Existence result to elliptic systems with nonstandard growth conditions, J. Math. Anal. Appl., 300 (2004), pp. 30-42.
5
[6] J.J. Liu and X.Y. Shi, Existence of three solutions for a class of quasilinear elliptic systems involving the (p(x), q(x))-Laplacian, Nonlinear Anal., 71 (2009), pp. 550-557.
6
[7] M. Mihailescue, Existence and multiplicity of solutions for a Neumann problem involving the p(x)-Laplace operator, Nonlinear Anal., 2007 (67), pp. 1419-1425.
7
[8] B. Ricceri, A three critical points theorem revisited, Nonlinear Anal., 70 (2009), pp. 3084-3089.
8
[9] B. Ricceri, A general variational principle and some of its applications, J. Comput. Appl. Math., 113 (2000), pp. 401-410.
9
[10] B. Ricceri, Existence of three solutions for a class of elliptic eigenvalue problem, Math. Comput. Modelling., 32 (2000), pp. 1485-1494.
10
[11] M. Ruzicka, Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Math, vol. 1784, Springer-Verlag, Berlin, 2000.
11
[12] H.H. Yin, Existence of three solutions for a Neumann problem involving the p(x)-Laplace operator, Math. Meth. Appl. Sci., 35 (2012), pp. 307-313.
12
[13] V.V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory, Math. USSR Izv. 29 (1987), pp. 33-36.
13
ORIGINAL_ARTICLE
Products Of EP Operators On Hilbert C*-Modules
In this paper, the special attention is given to the product of two modular operators, and when at least one of them is EP, some interesting results is made, so the equivalent conditions are presented that imply the product of operators is EP. Also, some conditions are provided, for which the reverse order law is hold. Furthermore, it is proved that $P(RPQ)$ is idempotent, if $RPQ$† has closed range, for orthogonal projections $P,Q$ and $R$.
https://scma.maragheh.ac.ir/article_28402_1be457bb812e3fe49f49618ae3136280.pdf
2018-04-01
61
71
10.22130/scma.2017.28402
Closed range
EP operators
Moore-Penrose inverse
Hilbert $C^*$-module
Javad
Farokhi-Ostad
javadfarrokhi90@gmail.com
1
Department of Mathematics, Faculty of Mathematics and Statistics, University of Birjand, Birjand, Iran.
LEAD_AUTHOR
Ali Reza
Janfada
ajanfada@birjand.ac.ir
2
Department of Mathematics, Faculty of Mathematics and Statistics, University of Birjand, Birjand, Iran.
AUTHOR
[1] S. Campbell and C.D. Meyer, Continuity properties of the Drazin pseudo inverse, Linear Algebra and Its Applications, 10 (1975), pp. 77-83.
1
[2] S. Campbell and C.D. Meyer, EP operators and generalized inverses, Canadian Math. Bull., 18 (1975), pp. 327-333.
2
[3] C.Y. Deng and H.K. Du, Representations of the Moore-Penrose inverse for a class of 2 by 2 block operator valued partial matrices, Linear and Multilinear Algebra, 58 (2010), pp. 15-26.
3
[4] D.S. Djordjevic, Further results on the reverse order law for generalized inverses, SIAM J. Matrix Anal. Appl., 29 (2007), pp. 1242-1246.
4
[5] D.S. Djordjevic and N.C. Dincic, Reverse order law for the Moore-Penrose inverse, J. Math. Anal. Appl., 361 (2010), pp. 252-261.
5
[6] J. Farokhi-ostad and M. Mohammadzadeh Karizaki, The reverse order law for EP modular operators, J. Math. Computer Sci. 16 (2016), pp. 412-418.
6
[7] M. Frank, Geometrical aspects of Hilbert C*-modules, Positivity, 1999, pp. 215-243.
7
[8] M. Frank, Self-duality and C*-reflexivity of Hilbert C*-modules, Z. Anal. Anwendungen, 1990, pp. 165-176.
8
[9] S. Izumino, The product of operators with closed range and an extension of the revers order law, Tohoku Math. J.,34 (2) (1982), pp. 43-52.
9
[10] E.C. Lance, Hilbert C*-Modules, LMS Lecture Note Series 210, Cambridge Univ. Press, 1995.
10
[11] M. Mohammadzadeh Karizaki and D.S. Djordjevic, Commuting C* modular operators, Aequationes Mathematicae 6 (2016), pp. 1103-1114.
11
[12] M. Mohammadzadeh Karizaki, M. Hassani, and M. Amyari, Moore-Penrose inverse of product operators in Hilbert C*-modules, Filomat, 8 (2016), pp. 3397-3402.
12
[13] M. Mohammadzadeh Karizaki, M. Hassani, M. Amyari, and M. Khosravi, Operator matrix of Moore-Penrose inverse operators on Hilbert C*-modules, Colloq. Math., 140 (2015), pp. 171-182.
13
[14] M.S. Moslehian, K. Sharifi, M. Forough, and M. Chakoshi, Moore-Penrose inverse of Gram operator on Hilbert C*-modules, Studia Math., 210 (2012), pp. 189-196.
14
[15] G.J. Murphy, C*-algebras and operator theory, Academic Press Inc., Boston, MA, 1990.
15
[16] K. Sharifi, The product of operators with closed range in Hilbert C*-modules, Linear Algebra Appl., 435 (2011), pp. 1122-1130.
16
[17] K. Sharifi, EP modular operators and their products, J. Math. Anal. Appl., 419 (2014), pp. 870-877.
17
[18] K. Sharifi and B. Ahmadi Bonakdar, The reverse order law for Moore-Penrose inverses of operators on Hilbert C* modules, Bull. Iran. Math. Soc., 42 (2016), pp. 53- 60.
18
[19] Q. Xu and L. Sheng, Positive semi-definite matrices of adjointable operators on Hilbert C*-modules, Linear Algebra Appl. 428 (2008), pp. 992-1000.
19
ORIGINAL_ARTICLE
$C^{*}$-semi-inner product spaces
In this paper, we introduce a generalization of Hilbert $C^*$-modules which are pre-Finsler modules, namely, $C^{*}$-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will be considered. We then study bounded linear operators on $C^{*}$-semi-inner product spaces.
https://scma.maragheh.ac.ir/article_28403_6d1882e6bcbd32d35db66b8ee540b844.pdf
2018-04-01
73
83
10.22130/scma.2017.28403
Semi-inner product space
Hilbert $C^*$-module
$C^*$-algebra
Saeedeh
Shamsi Gamchi
saeedeh.shamsi@gmail.com
1
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 ,Tehran, Iran.
LEAD_AUTHOR
Mohammad
Janfada
mjanfada@gmail.com
2
Department of Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad Iran.
AUTHOR
Asadollah
Niknam
dassamankin@yahoo.co.uk
3
Department of Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad Iran.
AUTHOR
[1] M. Amyari and A. Niknam, A note on Finsler modules, Bulletin of the Iranian Mathematical Society, 29 (2003), pp. 77-81.
1
2
[2] D. Bakic and B. Guljas, On a class of module maps of Hilbert C*-modules, Mathematica communications, 7 2 (2002), pp. 177-192.
3
4
[3] G. Birkhoff, Orthogonality in linear metric spaces, Duke Math. J., 1 (1935), pp. 169-172.
5
6
[4] S.S. Dragomir, Semi-Inner Products and Applications, Nova Science Publishers, Hauppauge, New York, 2004.
7
8
[5] S.S. Dragomir, J.J. Koliha, and Melbourne, Two mappings related to semi-inner products and their applications in geometry of normed linear spaces, Applications of Mathematics, 45 (2000), pp. 337-355.
9
10
[6] S.G. El-Sayyad and S.M. Khaleelulla , *-semi-inner product algebras of type(p), Zb. Rad. Prirod. Mat. Fak. Ser. Mat., 23 (1993), pp. 175-187.
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12
[7] G.D. Faulkner, Representation of linear functionals in a Banach space, Rocky Mountain J. Math., 7 (1977), pp. 789-792.
13
14
[8] J.R. Giles, Classes of semi-inner-product spaces, Trans. Amer. Math. Soc., 129 (1967), pp. 436-446.
15
16
[9] R.C. James, Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc., 61 (1947), pp. 265-292.
17
18
[10] B.E. Johnson, Centralisers and operators reduced by maximal ideals, J. London Math. Soc., 43 (1986), pp. 231-233.
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20
[11] I. Kaplansky, Modules over operator algebras, Amer. J. Math., (75) (1953), pp. 839-858.
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[12] D.O. Koehler, A note on some operator theory in certain semi-inner-product spaces, Proc. Amer. Math. Soc., 30 (1971), pp. 363-366.
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24
[13] G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc., 100 (1961), pp. 29-43.
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26
[14] G. Lumer, On the isometries of reflexive Orlicz spaces, Ann. Inst. Fourier (Grenoble)., 13 (1963), pp. 99-109.
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28
[15] E.C. Lance, Hilbert C*-modules . a toolkit for operator algebraists, London Math. Soc. Lecture Note Series, Cambridge Univ. Press, Cambridge, 1995.
29
30
[16] B. Nath, On generalization of semi-inner product spaces, Math. J. Okayama Univ., 15 (1971), pp. 1-6.
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32
[17] E. Pap and R. Pavlovic, Adjoint theorem on semi-inner product spaces of type (p), Zb. Rad. Prirod. Mat. Fak. Ser. Mat., 25 (1995), pp. 39-46.
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[18] W.L. Paschke, Inner product modules over B*-algebras, Trans. Amer. Math. Soc., 182 (1973), pp. 443-468.
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[19] N.C. Phillips and N. Weaver, Modules with norms which take values in a C*-algebra, Pacific J. of Maths., 185 (1998), pp. 163-181.
37
[20] C. Puttamadaiah and H. Gowda, On generalised adjoint abelian operators on Banach spaces, Indian J. Pure Appl. Math., 17 (1986), pp. 919-924.
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[21] M.A. Rieffel, Induced representations of C*-algebras, Adv. Math., 13 (1974), pp. 176-257.
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[22] B. Rzepecki, On fixed point theorems of Maia type, Publications de l'Institut Mathématique, 28 (1980), pp. 179-186.
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[23] E. Torrance, Strictly convex spaces via semi-inner-product space orthogonality, Proc. Amer. Math. Soc., 26 (1970), pp. 108-110.
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45
[24] H. Zhang and J. Zhang, Generalized semi-inner products with applications to regularized learning, J. Math. Anal. Appl., 372 (2010), pp. 181-196.
46
ORIGINAL_ARTICLE
Some fixed point theorems for $C$-class functions in $b$-metric spaces
In this paper, via $C$-class functions, as a new class of functions, a fixed theorem in complete $b$-metric spaces is presented. Moreover, we study some results, which are direct consequences of the main results. In addition, as an application, the existence of a solution of an integral equation is given.
https://scma.maragheh.ac.ir/article_28505_afd91ddcdba1fe1a635f69bdc0a74c71.pdf
2018-04-01
85
96
10.22130/scma.2017.28505
Fixed point
Complete metric space
$b$-metric space
$C$-class function
Arslan
Hojat Ansari
analsisamirmath2@gmail.com
1
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
AUTHOR
Abdolrahman
Razani
razani@ipm.ir
2
Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.
LEAD_AUTHOR
[1] A. Aghajani, M. Abbas, and J.R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 4 (2014), pp. 941-960.
1
[2] A.H. Ansari, Note on φ-ψ-contractive type mappings and related fixed point, The 2nd regional conference on mathematics and applications, PNU, 2014, pp. 377-380.
2
[3] A.H. Ansari, S. Chandok, and C. Ionescu, Fixed point theorems on b-metric spaces for weak contractions with auxiliary functions, J. Inequal. Appl., 429 (2014), pp. 1-17.
3
[4] H. Aydi, M. Bota, E. Karapinar, and S. Mitrovic, A fixed point theorem for set-valued quasicontractions in b-metric spaces, Fixed Point Theory Appl., 88 (2012).
4
[5] I.A. Bakhtin, The contraction mapping principle in quasimetric spaces (Russian), Func. An., Gos. Ped. Inst. Unianowsk, 30 (1989), pp. 26-37.
5
[6] M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Modern Math., 4 (2009), pp. 285-301.
6
[7] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations int egrales, Fund. Math., 3 (1922), pp. 133-181.
7
[8] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inf. Univ. Ostrav., 1 (1993), pp. 5-11.
8
[9] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), pp. 263-276.
9
[10] Z.M. Fadail, A.G.B. Ahmad, A.H. Ansari, S. Radenovic, and M. Rajovic, Some common fixed point results of mappings in 0-σ-complete metric-like spaces via new function, Appl. Math. Sci., 9 (2015), pp. 4109-4127.
10
[11] R.H. Haghi, Sh. Rezapour, and N. Shahzad, Some fixed point generalizations are not real generalizations, Nonlinear Anal., 74 (2011), pp. 1799-1803.
11
[12] N. Hussain, V. Parvaneh, J.R. Roshan, and Z. Kadelburg, Fixed points of cyclic weakly (ψ, φ, L, A, B)-contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory Appl., 256 (2013), pp. 1-18.
12
[13] M.S. Khan, M. Swaleh, and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), pp. 1-9.
13
ORIGINAL_ARTICLE
Convergence of Integro Quartic and Sextic B-Spline interpolation
In this paper, quadratic and sextic B-splines are used to construct an approximating function based on the integral values instead of the function values at the knots. This process due to the type of used B-splines (fourth order or sixth order), called integro quadratic or sextic spline interpolation. After introducing the integro quartic and sextic B-spline interpolation, their convergence is discussed. The interpolation errors are studied. Numerical results illustrate the efficiency and effectiveness of the new interpolation method.
https://scma.maragheh.ac.ir/article_27153_746eb3f7b1690e6f4e7d778acb54a765.pdf
2018-04-01
97
108
10.22130/scma.2017.27153
Integro interpolation quartic B-spline
Integro interpolation sextic B-spline
Convergence
Jafar
Ahmadi Shali
j_ahmadishali@tabrizu.ac.ir
1
Department of Statistics, Faculty of Mathematical Science, University of Tabriz, Tabriz, Iran.
LEAD_AUTHOR
Ahmadreza
Haghighi
ah.haghighi@gamil.com
2
Department of Mathematics, Faculty of Science, Technical and Vocational University(TVU), Tehran, Iran and Department of Mathematics, Faculty of Science, Urmia University of technology, P.O.Box 57166-17165, Urmia-Iran.
AUTHOR
Nasim
Asghary
nasim.asghary@gmail.com
3
Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran.
AUTHOR
Elham
Soleymani
elham13829@gamil.com
4
Department of Mathematics, Faculty of Science, Urmia University of technology, P.O.Box 57166-17165, Urmia, Iran.
AUTHOR
[1] C.de Boor, A Practical Guide to Spline Interpolation, Springer-Verlag, New York, 1978.
1
[2] A.R. Haghighi and M. Roohi, The fractional cubic spline interpolation without using the derivative values, Indian Journal of Science and Technology, 5 (2012), pp. 3433-3439.
2
[3] H. Behforooz, Approximation by integro cubic splines, Appl. Math. Comput., 175 (2006), pp. 8-15.
3
[4] H. Behforooz, Interpolation by integro quintic splines Appl. Math. Comput., 216 (2010), pp. 364-367.
4
[5] F.G. Lang, X.P, On integro quartic spline interpolation, Appl. Math. Comput., 236 (2012), pp. 4214-4226.
5
[6] T. Wu and X.Zhang, Integro sextic spline interpolation and its super convergence, Appl. Math. Comput., 219 (2013), pp. 6431-6436.
6
[7] R.H. Wang, Numerical Approximation, Higher Education Press, Higher Education Press, Beijing, 1999.
7
[8] L. Schumaker, Spline Functions: Basic Theory, Cambridge University Press, Cambridge, 2007.
8
ORIGINAL_ARTICLE
Somewhat pairwise fuzzy $\alpha$-irresolute continuous mappings
The concept of somewhat pairwise fuzzy $\alpha$-irresolute continuous mappings and somewhat pairwise fuzzy irresolute $\alpha$-open mappings have been introduced and studied. Besides, some interesting properties of those mappings are given.
https://scma.maragheh.ac.ir/article_28222_b2ea806bbb58f3ed6cb833cf34043406.pdf
2018-04-01
109
118
10.22130/scma.2017.28222
Somewhat pairwise fuzzy $alpha$-irresolute continuous mapping
Somewhat pairwise fuzzy irresolute $alpha$-open mapping
Ayyarasu
Swaminathan
asnathanway@gmail.com
1
Department of Mathematics (FEAT),Annamalai University, Annamalainagar, Tamil Nadu-608 002, India.
LEAD_AUTHOR
[1] K.K. Azad, On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl., 82 (1981), pp. 14-32.
1
[2] C.L. Chang, Fuzzy topological spaces, J.Math.Anal.Appl.,24 (1968), pp. 182-190.
2
[3] K.R. Gentry and Hughes B. Hoyle, III, Somewhat continuous functions, Czech. Math. Journal 21 (1971), pp. 5-12.
3
[4] Y.B. Im, J.S. Lee, and Y.D. Cho, Somewhat fuzzy α-irresolute continuous mappings, Far East J. Math. Sci.70 (2012), pp. 145-155.
4
[5] A. Kandil and M.E. El-Shafee, Biproximities and fuzzy bitopological spaces, Simon Steviv, 63 (1989), pp. 4566.
5
[6] R. Prasad, S. Thakur, and R.K. Sand, Fuzzy α-irresolute mappings, J. Fuzzy Math. 2 (1994), pp. 335-339.
6
[7] M.K. Singal and N. Rajvanshi, Fuzzy α-sets and alpha-continuous maps, Fuzzy Sets and Systems, 48 (1992), pp. 383-390.
7
[8] G. Thangaraj and G. Balasubramanian, On somewhat fuzzy α-continuous functions, J. Fuzzy Math. 16 (2008), pp. 641-651.
8
[9] L.A. Zadeh, Fuzzy sets, Inform. And Control, 8 (1965), pp. 338-353.
9
ORIGINAL_ARTICLE
$L$-Topological Spaces
By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of L-topological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathematical notion. Our emphasis would be concentrated on the well understood classical connectedness, quotient and compactness notions, where we prove the Thychonoff's theorem and connectedness property for ultra product of $L$-compact and $L$-connected topological spaces, respectively.
https://scma.maragheh.ac.ir/article_28387_de42aeb44cc0345bcda542f42caad0ac.pdf
2018-04-01
119
133
10.22130/scma.2017.28387
Compact Spaces
Connected Spaces
Frame
Ali
Bajravani
bajravani1305@gmail.com
1
Department of Mathematics, Faculty of Basic Sciences, Azarbaijan Shahid Madani University, Tabriz, I. R. Iran.
LEAD_AUTHOR
[1] A. Bajravani and A. Rastegar, On the Smoothness of Functors, Iranian Journal of Mathematical Sciences and Informatics., 5(2010), pp. 27-39.
1
[2] E. Bredon Glen, Topology and Geometry, Graduate Texts in Mathematics 139, Springer, 1993.
2
[3] S. Burris and H.P. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, 1981.
3
[4] A. Hatcher, Algebraic Topology, Cambridge University Press; 2002.
4
[5] J.R. Munkres, Topology, Second Edition, Prentice Hall, Inc; 2000.
5
[6] D.G. Wright, Thychonoff's Theorem, Proceedings of the A. M. S., 120, 1994.
6
ORIGINAL_ARTICLE
Fuzzy $e$-regular spaces and strongly $e$-irresolute mappings
The aim of this paper is to introduce fuzzy ($e$, almost) $e^{*}$-regular spaces in $\check{S}$ostak's fuzzy topological spaces. Using the $r$-fuzzy $e$-closed sets, we define $r$-($r$-$\theta$-, $r$-$e\theta$-) $e$-cluster points and their properties. Moreover, we investigate the relations among $r$-($r$-$\theta$-, $r$-$e\theta$-) $e$-cluster points, $r$-fuzzy ($e$, almost) $e^{*}$-regular spaces and their functions.
https://scma.maragheh.ac.ir/article_28031_3494182d1a8d67a79d2f6930e9405e49.pdf
2018-04-01
135
156
10.22130/scma.2017.28031
Fuzzy topology
$r$-fuzzy $e$-open (closed) sets
$r$-($r$-$theta$-
$r$-$etheta$-) $e$-cluster points
$r$-fuzzy ($e$
almost) $e^{*}$-regular spaces
(strongly
$theta$-) $e$-irresolute mappings
Veerappan
Chandrasekar
vckkc3895@gmail.com
1
Department of Mathematics, Kandaswami Kandar's College, P-velur-638 182, Tamil Nadu, India.
AUTHOR
Somasundaram
Parimala
pspmaths@gmail.com
2
Research Scholar (Part Time), Department of Mathematics, Kandaswami Kandar's College, P-velur-638 182, Tamil Nadu, India.
LEAD_AUTHOR
[1] C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), pp. 182-190.
1
[2] K.C. Chattopadhyay, R.N. Hazra, and S.K. Samanta, Gradation of openness, Fuzzy Sets and Systems, 49 (1992), pp. 237-242.
2
[3] K.C. Chattopadhyay and S.K. Samanta, Fuzzy topology, Fuzzy Sets and Systems, 54 (1993), pp. 207-212.
3
[4] Y.C. Kim, δ-closure operators in fuzzy bitopological spaces, Far East J. Math. Sci., 2 (2000), pp. 791-808.
4
[5] Y.C. Kim, r-fuzzy α-open and r-fuzzy preopen sets in fuzzy bitopological spaces, Far East J. Math. Sci. Spec, (2000), pp. 315-334.
5
[6] Y.C. Kim and S.E. Abbas, Several types of fuzzy regular spaces, Indian J. Pure and Appl. Math., 35 (2004), pp. 481-500.
6
[7] Y.C. Kim and B. Krsteska, Fuzzy P-regular spaces, The Journal of Fuzzy Mathematics, 14 (2006), pp. 701-722.
7
[8] Y.C. Kim and J.W. Park, r-fuzzy δ-closure and r-fuzzy θ-closure sets, J. Korea Fuzzy Logic and Intelligent systems, 10 (2000), pp. 557-563.
8
[9] Y.C. Kim, A.A. Ramadan, and S. E. Abbas r-fuzzy strongly preopen sets in fuzzy topological spaces, Math. Vesnik, 55 (2003), pp. 1-13.
9
[10] T. Kubiak, On fuzzy topologies, Ph.D. Thesis, A. Mickiewicz, Poznan, 1985.
10
[11] A.A. Ramadan, Smooth topological spaces, Fuzzy Sets and Systems, 48 (1992), pp. 371-375.
11
[12] D. Sobana, V. Chandrasekar, and A. Vadivel, Fuzzy e-continuity in Sostak's fuzzy topological spaces, (Submitted).
12
[13] A.P. Sostak, Basic structures of fuzzy topology, J. Math. Sci., 78 (1996), pp. 662-701.
13
[14] A.P. Sostak, Two decades of fuzzy topology: Basic ideas, Notion and results, Russian Math. Surveys, 44 (1989), pp. 125-186.
14
[15] A.P. Sostak, On a fuzzy topological structure, Rend. Circ. Matem. Palermo Ser II, 11 (1986), pp. 89-103.
15