University of MaraghehSahand Communications in Mathematical Analysis2322-580710120180401On generalized topological molecular lattices1152714810.22130/scma.2017.27148ENNarges NazariDepartment of Mathematics, University of Hormozgan, Bandarabbas, Iran.Ghasem MirhosseinkhaniDepartment of Mathematics, Sirjan University of Technology, Sirjan, Iran.Journal Article20161220In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580710120180401Similar generalized frames17282462810.22130/scma.2017.24628ENAzadeh AlijaniDepartment of Mathematics, Faculty of Science,
Vali-e-Asr University of Rafsanjan, P.O. Box 7719758457, Rafsanjan, Iran.Journal Article20160915Generalized 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580710120180401On $L^*$-proximate order of meromorphic function29352312710.22130/scma.2016.23127ENSanjib DattaDepartment of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.Tanmay BiswasRajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.Journal Article20160202In this paper we introduce the notion of $L^{* }$-proximate order of meromorphic function and prove its existence.University of MaraghehSahand Communications in Mathematical Analysis2322-580710120180401The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions37462715210.22130/scma.2017.27152ENLeila NasiriDepartment of Mathematics and computer science, Faculty of science, Lorestan University, Khorramabad, Iran.Ali SameripourDepartment of Mathematics and computer science, Faculty of science, Lorestan University, Khorramabad, Iran.Journal Article20170109Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580710120180401Existence of three solutions for a class of quasilinear elliptic systems involving the $p(x)$-Laplace operator47602791510.22130/scma.2017.27915ENAli TaghaviDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.Ghasem Alizadeh AfrouziDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.Horieh GhorbaniDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.Journal Article20161124The 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580710120180401Products Of EP Operators On Hilbert C*-Modules61712840210.22130/scma.2017.28402ENJavad Farokhi-OstadDepartment of Mathematics, Faculty of Mathematics and Statistics, University of Birjand, Birjand, Iran.Ali Reza JanfadaDepartment of Mathematics, Faculty of Mathematics and Statistics, University of Birjand, Birjand, Iran.Journal Article20161013In 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 $RPQ$<sup>†</sup> has closed range, for orthogonal projections $P,Q$ and $R$.University of MaraghehSahand Communications in Mathematical Analysis2322-580710120180401$C^{*}$-semi-inner product spaces73832840310.22130/scma.2017.28403ENSaeedeh Shamsi GamchiDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697 ,Tehran, Iran.Mohammad JanfadaDepartment of Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad Iran.Asadollah NiknamDepartment of Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad Iran.Journal Article20160526In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580710120180401Some fixed point theorems for $C$-class functions in $b$-metric spaces85962850510.22130/scma.2017.28505ENArslan Hojat AnsariDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.Abdolrahman RazaniDepartment of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.Journal Article20170225In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580710120180401Convergence of Integro Quartic and Sextic B-Spline interpolation971082715310.22130/scma.2017.27153ENJafar Ahmadi ShaliDepartment of Statistics, Faculty of Mathematical Science, University of Tabriz, Tabriz, Iran.Ahmadreza HaghighiDepartment 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.Nasim AsgharyDepartment of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran.Elham SoleymaniDepartment of Mathematics, Faculty of Science, Urmia University of technology, P.O.Box 57166-17165, Urmia, Iran.Journal Article20170727In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580710120180401Somewhat pairwise fuzzy $alpha$-irresolute continuous mappings1091182822210.22130/scma.2017.28222ENAyyarasu SwaminathanDepartment of Mathematics (FEAT),Annamalai University, Annamalainagar, Tamil Nadu-608 002, India.Journal Article20160718The 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580710120180401$L$-Topological Spaces1191332838710.22130/scma.2017.28387ENAli BajravaniDepartment of Mathematics, Faculty of Basic Sciences, Azarbaijan Shahid Madani University, Tabriz, I. R. Iran.Journal Article20170212By 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580710120180401Fuzzy $e$-regular spaces and strongly $e$-irresolute mappings1351562803110.22130/scma.2017.28031ENVeerappan ChandrasekarDepartment of Mathematics, Kandaswami Kandar's College, P-velur-638 182, Tamil Nadu, India.Somasundaram ParimalaResearch Scholar (Part Time), Department of Mathematics, Kandaswami Kandar's College, P-velur-638 182, Tamil Nadu, India.Journal Article20160629The 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 $r$-($r$-$theta$-, $r$-$etheta$-) $e$-cluster points and their properties. Moreover, we investigate the relations among $r$-($r$-$theta$-, $r$-$etheta$-) $e$-cluster points, $r$-fuzzy ($e$, almost) $e^{*}$-regular spaces and their functions.