University of MaraghehSahand Communications in Mathematical Analysis2322-580719120220201An Introduction to Spectral Theory of Bounded Linear Operators in Intuitionistic Fuzzy Pseudo Normed Linear Space11324811510.22130/scma.2021.531698.942ENBivasDindaDepartment of Mathematics, Mahishamuri Ramkrishna Vidyapith,
Howrah 711401, WB, India and Department of Mathematics, Kazi Nazrul University,
Asansol 713340, WB, India0000-0002-9761-4820Santanu KumarGhoshDepartment of Mathematics, Kazi Nazrul University,
Asansol 713340, WB, India.0000-0001-8707-6814Tapas KumarSamantaDepartment of Mathematics, Uluberia College,
Howrah 711315, WB, India0000-0001-8728-0356Journal Article20210606In this paper, focus is on the study of spectrum and the spectral properties of bounded linear operators in intuitionistic fuzzy pseudo normed linear spaces(IFPNLS). It is done by studying regular value, resolvent set, spectrum of a linear operator in IFPNLS. Also, some properties of spectrum and resolvent of strongly intuitionistic fuzzy bounded(IFB) linear operators in IFPNLS are being developed. It is observed that, for a linear operator $P$ in an IFPNLS, the resolvent set $\rho(P)$ and spectrum $\sigma(P)$ are nonempty, $\rho(P)$ is open and $\sigma(P)$ is closed set.https://scma.maragheh.ac.ir/article_248115_9c4220c7962c7545aa03eac8c587c77f.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719120220201A New Three-Step Mixed-Type Implicit Iterative Scheme with Errors for Common Fixed Points of Nonexpansive and Uniformly $L$--Lipschitzian Asymptotically Generalized $\Phi$-Hemicontractive Mappings154024890610.22130/scma.2021.140147.873ENAustine EfutOfemDepartment of Mathematics, University of Uyo, Uyo, Nigeria.0000-0001-8064-2326Donatus IkechiIgbokweDepartment of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria.Journal Article20201119In this paper, we introduce a three-step implicit iteration scheme with errors for finite families of nonexpansive and uniformly $L$-Lipschitzian asymptotically generalized $\Phi$-hemicontractive mappings in real Banach spaces. Our new implicit iterative scheme properly includes several well known iterative schemes in the literature as its special cases. The results presented in this paper extend, generalize and improve well known results in the existing literature.https://scma.maragheh.ac.ir/article_248906_f221a5bdef500a8412d490ed860e5f7d.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719120220201New Integral Inequalities Relating to a General Integral Operators Through Monotone Functions415624890810.22130/scma.2021.521013.887ENBouharketBenaissaFaculty of Material Sciences, University of Tiaret and
Laboratory of Informatics and Mathematics, University of Tiaret-Algeria.0000-0002-1195-6169AbdelkaderSenouciDepartment of Mathematics, University of Tiaret and
Laboratory of Informatics and Mathematics, University of Tiaret-Algeria.Journal Article20201212Weighted integral inequalities for general integral operators on monotone positive functions with parameters $p$ and $q$ are established in [4]. The aim of this work is to extend the results to different cases of these parameters, in particular for negative $p$ and $q$. We give some new lemmas which will be frequently used in the proofs of the main theorems.https://scma.maragheh.ac.ir/article_248908_c71459478de6b05d35d315afdf30b0fd.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719120220201The Operators' Theorems on Fuzzy Topological Spaces577624891010.22130/scma.2021.533260.953ENMortezaSaheliDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Seyed Ali MohammadMohsenialhosseiniDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.HadiSaeidi GoraghaniDepartment of Mathematics, Payame Noor University, Tehran, Iran.Journal Article20210702Three types of fuzzy topologies defined on fuzzy normed linear spaces are considered in this paper. First, the relationship<br />between fuzzy continuity of linear operators and fuzzy boundedness is investigated. The uniform boundedness theorem is then discussed, so too is the norm of a linear operator. Finally, the open mapping theorem is proved for each of the three defined fuzzy topologies, and the closed graph theorem is studied.https://scma.maragheh.ac.ir/article_248910_bb60da7fe1faac46d376a3f7119556fd.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719120220201Some Results on Cesàro summability in Intuitionistic Fuzzy $n$-normed linear Spaces778724896810.22130/scma.2021.529567.933ENPradipDebnathDepartment of Applied Science and Humanities, Assam University, Silchar, Cachar, Assam - 788011, India.0000-0003-0097-0819Journal Article20210502The concept of summability plays a central role in finding formal solutions of partial differential equations. In this paper, we introduce the concept of Cesàro summability in an intuitionistic fuzzy $n$-normed linear space (IFnNLS). We show that Cesàro summability method is regular in an IFnNLS, but Cesàro summability does not imply usual convergence in general. Further, we search for additional conditions under which the converse holds.https://scma.maragheh.ac.ir/article_248968_7ea9c44f0654c01e7983143d67b80b12.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719120220201Categorical Properties of Down Closed Embeddings899924940610.22130/scma.2022.545343.1038ENLeilaShahbazDepartment of Mathematics, University of Maragheh, Maragheh,
55181-83111, Iran.0000-0001-6312-6231Journal Article20211222Let $\mathcal M$ be a class of (mono)morphisms in a category $\mathcal A$. To study mathematical notions, such as injectivity, tensor products, flatness, one needs to have some categorical and algebraic information about the pair (${\mathcal A}$,${\mathcal M}$).<br />In this paper, we take $\mathcal A$ to be the category {\bf Pos}-$S$ of $S$-posets over a posemigroup $S$, and ${\mathcal M}_{dc}$ to be the class of down closed embeddings and study the categorical properties, such as limits and colimits, of the pair (${\mathcal A}$,${\mathcal M}$). Injectivity with respect to this class of monomorphisms have been studied by Shahbaz et al., who used it to obtain information about regular injectivity.https://scma.maragheh.ac.ir/article_249406_3d57569204846263835eb8b5bf190414.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719120220201L$_p$-C$^*$-Semi-Inner Product Spaces10111724941710.22130/scma.2021.526207.918ENZakiyeKhaliliDepartment of Mathematics, University of Birjand, Birjand, P. O. Box 414, 9717851367, Birjand, Iran.https://orcid.org/00AlirezaJanfadaDepartment of Mathematics, University of Birjand, Birjand, P. O. Box 414, 9717851367, Birjand, Iran.0000-0003-3224-3288Mohammad RezaMiriDepartment of Mathematics, University of Birjand, Birjand, P. O. Box 414, 9717851367, Birjand, Iran.0000-0001-9379-1064MohsenNiaziDepartment of Mathematics, University of Birjand, Birjand, P. O. Box 414, 9717851367, Birjand, Iran.Journal Article20210306This article introduces the notion of L$_p$-C$^*$-semi-inner product space, a generalization of the concept of C$^*$-semi-inner product space introduced by Gamchi et al., where we consider H\"{o}lder's inequality instead of Cauchy Schwartz' inequality. We establish some basic results L$_p$-C$^*$-semi-inner product spaces, analogous to those valid for C$^*$-semi-inner product spaces and Hilbert C$^*$-modules.https://scma.maragheh.ac.ir/article_249417_5b0ef11400191836daa3c4b5bc34b439.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719120220201Positivity of Integrals for Higher Order $\nabla-$Convex and Completely Monotonic Functions11913724958510.22130/scma.2021.527460.926ENFarazMehmoodDepartment of Mathematics, Dawood University of Engineering and Technology, New M. A. Jinnah Road, Karachi-74800, Pakistan.0000-0002-9536-3300Asif RazaKhanDepartment of Mathematics, University of Karachi, University Road, Karachi-75270 Pakistan.MuhammadAdnanDepartment of Mathematics, University of Karachi, University Road, Karachi-75270 Pakistan.Journal Article20210403We extend the definitions of $\nabla-$convex and completely monotonic functions for two variables. Some general identities of Popoviciu type integrals $\int P(y)f(y) dy$ and $\int \int P(y,z) f(y,z) dy dz$ are deduced. Using obtained identities, positivity of these expressions are characterized for higher order $\nabla-$convex and completely monotonic functions. Some applications in terms of generalized Cauchy means and exponential convexity are given.https://scma.maragheh.ac.ir/article_249585_172a7aeb2e4fe6ea55ee687557aa2805.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719120220201Study on Some Integral Inequalities for Pseudo-Integrals13915925392610.22130/scma.2022.557671.1148ENBayazDarabyDepartment of Mathematics, University of Maragheh, P. O. Box 55181-83111, Maragheh, Iran.0000-0001-6872-8661Journal Article20220712In this paper, we express and prove Stolarsky, Feng Qi and Markov type inequalities for two classes of pseudo-integrals. One of them concerning the pseudo-integrals based on a function reduces on the g-integral where pseudo-operations are defined by a monotone and continuous function $g$. The other one concerns the pseudo-integrals based on a semiring $( [a, b], \max, \odot )$, where $\odot$ is generated. The integral inequalities are appling in multivariate approximation theory and probability theory and etc.https://scma.maragheh.ac.ir/article_253926_36aef141907c9db00b5142f1c944d458.pdf