Sahand Communications in Mathematical Analysis
https://scma.maragheh.ac.ir/
Sahand Communications in Mathematical Analysisendaily1Tue, 01 Feb 2022 00:00:00 +0330Tue, 01 Feb 2022 00:00:00 +0330An Introduction to Spectral Theory of Bounded Linear Operators in Intuitionistic Fuzzy Pseudo Normed Linear Space
https://scma.maragheh.ac.ir/article_248115.html
In 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.A New Three-Step Mixed-Type Implicit Iterative Scheme with Errors for Common Fixed Points of Nonexpansive and Uniformly $L$--Lipschitzian Asymptotically Generalized $\Phi$-Hemicontractive Mappings
https://scma.maragheh.ac.ir/article_248906.html
In 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.New Integral Inequalities Relating to a General Integral Operators Through Monotone Functions
https://scma.maragheh.ac.ir/article_248908.html
Weighted 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.The Operators' Theorems on Fuzzy Topological Spaces
https://scma.maragheh.ac.ir/article_248910.html
Three types of fuzzy topologies defined on fuzzy normed linear spaces are considered in this paper. First, the relationshipbetween 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.Some Results on Cesàro summability in Intuitionistic Fuzzy $n$-normed linear Spaces
https://scma.maragheh.ac.ir/article_248968.html
The concept of summability plays a central role in finding formal solutions of partial differential equations. In this paper, we introduce the concept of Ces&agrave;ro summability in an intuitionistic fuzzy $n$-normed linear space (IFnNLS). We show that Ces&agrave;ro summability method is regular in an IFnNLS, but &nbsp;Ces&agrave;ro summability does not imply usual convergence in general. Further, we search for additional conditions under which the converse holds.Categorical Properties of Down Closed Embeddings
https://scma.maragheh.ac.ir/article_249406.html
Let $\mathcal M$ be a &nbsp;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 (${\mathcal A}$,${\mathcal M}$).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 &nbsp;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 &nbsp;information about regular injectivity.L$_p$-C$^*$-Semi-Inner Product Spaces
https://scma.maragheh.ac.ir/article_249417.html
This article introduces the notion of L$_p$-C$^*$-semi-inner product space, a generalization of the concept of C$^*$-semi-inner product space &nbsp;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.Positivity of Integrals for Higher Order $\nabla-$Convex and Completely Monotonic Functions
https://scma.maragheh.ac.ir/article_249585.html
We 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 $\int \int P(y,z) f(y,z) dy &nbsp; dz$ are deduced. Using obtained identities, positivity of these expressions are characterized for &nbsp;higher order $\nabla-$convex and completely monotonic functions. Some applications in terms of generalized Cauchy means and exponential convexity are given.On New Integral Inequalities via Geometric-Arithmetic Convex Functions with Applications
https://scma.maragheh.ac.ir/article_250962.html
In this study, new Hermite-Hadamard type inequalities are generated for geometric-arithmetic functions with the help of an integral equation proved for differentiable functions. In proofs, some classical integral inequalities, such as H\"{o}lder's inequality, basic definitions and known mathematical analysis procedures are used. The third part of the study includes various applications confirming the accuracy of the generated results. A brief conclusion of the study has been given in the last part of the paper.Fixed Point Results for $F$-Hardy-Rogers Contractions via Mann's Iteration Process in Complete Convex $b$-Metric Spaces
https://scma.maragheh.ac.ir/article_251665.html
In this paper, we give a definition of the $F$-Hardy-Rogers contraction of Nadler type by eliminating the conditions $(F3)$ and $(F4)$. And, we obtain some fixed point theorems for such mappings using Mann's iteration process in complete convex $b$-metric spaces. We also give an example in order to support the main results, &nbsp;which generalize some results in [5,6].Essential Norm of the Generalized Integration Operator from Zygmund Space into Weighted Dirichlet Type Space
https://scma.maragheh.ac.ir/article_251966.html
Let $H(\mathbb{D})$ be the space of all analytic functions on the open unit disc $\mathbb{D}$ in the complex plane $\mathbb{C}$. In this paper, we investigate the boundedness and compactness of the generalized integration operator$$I_{g,\varphi}^{(n)}(f)(z)=\int_0^z f^{(n)}(\varphi(\xi))g(\xi)\ d\xi,\quad z\in\mathbb{D},$$ from Zygmund space into weighted Dirichlet type space, where $\varphi$ is an analytic self-map of $\mathbb{D}$, $n\in\mathbb{N}$ and $g\in H(\mathbb{D})$. Also we give an estimate for the essential norm of the above operator.Bijections on the Unit Ball of $B(H)$ Preserving $^{\ast}$-Jordan Triple Product
https://scma.maragheh.ac.ir/article_251967.html
Let &nbsp;$ \mathcal{B}_1$ &nbsp;denote the closed unit ball of &nbsp;$\mathcal B(H)$, the von Neumann algebra of all bounded linear operators on a complex Hilbert space $H$ with $\dim H\geq 2$. Suppose that $\phi$ is a bijection on $ \mathcal{B}_1$ (with no linearity assumption) satisfying\begin{equation*}\phi(AB^{*}A)=\phi(A)\phi(B)^{*}\phi(A), \quad( A, B\in &nbsp;\mathcal{B}_1).\end{equation*}If $I$ and $\mathbb T$ denote the identity operator on $H$ and the unit circle in $\mathbb C$, respectively and if $\phi$ is continuous on $\{\lambda I: \lambda\in \mathbb T\}$, then we show that &nbsp;$\phi(I)$ is a unitary operator and $\phi(I)\phi$ extends to a linear or conjugate linear Jordan $^*$-automorphism on $\mathcal B(H)$. As a consequence, there is either a unitary or an antiunitary operator &nbsp; $U$ on $H$ such that $\phi(A)=\phi(I) UAU^*$, $(A\in {\mathcal B}_1)$ or $ \phi(A)=\phi(I) UA^*U^*$, $(A\in {\mathcal B}_1)$.Nearly $k-th$ Partial Ternary Cubic $*$-Derivations On Non-Archimedean $\ell$-Fuzzy $C^{*}$-Ternary Algebras
https://scma.maragheh.ac.ir/article_251968.html
In this paper, we investigate approximations of the $k-th$ partial ternary cubic derivations on non-Archimedean $\ell$-fuzzy Banach ternary algebras and non-Archimedean $\ell$-fuzzy $C^{*}$-ternary algebras. First, we study non-Archimedean and $\ell$-fuzzy spaces, and then &nbsp;prove the stability of partial ternary cubic $*$-derivations on non-Archimedean $\ell$-fuzzy $C^{*}$-ternary algebras. We therefore provide a link among different disciplines: fuzzy set theory, lattice theory, non-Archimedean spaces, and mathematical analysis.The Study of Felbin and $BS$ Fuzzy Normed Linear Spaces
https://scma.maragheh.ac.ir/article_252079.html
In this paper, we first show that the &nbsp;induced topologies by Felbin and Bag-Samanta type fuzzy norms on a linear space $X$ are equivalent. So all results in Felbin-fuzzy normed linear spaces are valid in Bag-Samanta fuzzy normed linear spaces and vice versa. Using this, we will be able to define a fuzzy norm on $FB(X,Y)$, the space of all fuzzy bounded linear operators from $X$ into $Y$, where $X$ and $Y$ are fuzzy normed linear spaces.