Sahand Communications in Mathematical Analysis
https://scma.maragheh.ac.ir/
Sahand Communications in Mathematical Analysisendaily1Wed, 01 Dec 2021 00:00:00 +0330Wed, 01 Dec 2021 00:00:00 +0330Introduction of Frame in Tensor Product of $n$-Hilbert Spaces
https://scma.maragheh.ac.ir/article_247537.html
We study the concept of frame in tensor product of &nbsp;$n$-Hilbert spaces as tensor product of &nbsp;$n$-Hilbert spaces is again an &nbsp;$n$-Hilbert space. We generalize some of the known results about bases to frames in this new Hilbert space. A relationship between frame and bounded linear operator in tensor product of &nbsp;$n$-Hilbert spaces is studied. Finally,\;the dual frame in tensor product of &nbsp;$n$-Hilbert spaces is discussed.Boundary Value Problems in Thermo Viscoplasticity
https://scma.maragheh.ac.ir/article_246178.html
In this work, we study two uncoupled quasistatic problems for thermo viscoplastic materials. In the model of the equation of generalised thermo viscoplasticity, both the elastic and the plastic rate of deformation depend on a parameter $\theta $ which may be interpreted as the absolute temperature. The boundary conditions considered here as displacement-traction conditions as well as unilateral contact conditions. We establish a variational formulation for the model and we prove the existence of a unique weak solution to the problem, reducing the isotherm problem to an ordinary differential equation in a Hilbert space.Fixed Point Theorems for Fuzzy $(\gamma,\beta)$-Contractions in non-Archimedean Fuzzy Metric Spaces
https://scma.maragheh.ac.ir/article_246750.html
In this paper, &nbsp;we introduce new concepts of fuzzy $(\gamma,\beta )$-contraction and prove some fixed point results for fuzzy $(\gamma,\beta )$-contractions in complete non-Archimedean fuzzy metric spaces. Later, we define a fuzzy $(\gamma,\beta )$-weak contraction and establish some new fixed point results for fuzzy $(\gamma,\beta )$-weak contractions. Also, some examples are supplied in order to support the useability of ourresults.$\mathcal{I}$-convergence in Fuzzy Cone Normed Spaces
https://scma.maragheh.ac.ir/article_246752.html
The aim of this paper is to define and study the concept of $\mathcal{I}$-convergence in fuzzy cone normed space which is a generalization of R. Saadati and S. M. Vaezpour type fuzzy normal space. We also obtained some basic properties of $\mathcal{I}$-convergence. In fuzzy cone normed space, $\mathcal{I}$-limit point and $\mathcal{I}$-cluster point were defined and studied.Weighted Cebysev Type Inequalities for Double Integrals and Application
https://scma.maragheh.ac.ir/article_246902.html
The purpose of this article is to generalize Cebysev type inequalities for double integrals involving a weight function.By using an integral transform that is a weighted Montgomery identity, we obtained a generalized form of weighted Cebysev type inequalities in $L_m,\, m\geq 1$ norm of differentiable functions. Also, we give some applications of the probability density function.Investigation of the Boundary Layers of the Singular Perturbation Problem Including the Cauchy-Euler Differential Equation
https://scma.maragheh.ac.ir/article_247538.html
In this paper, for a singular perturbation problem consist of the Cauchy-Euler equation with local and non-local boundary conditions. We investigate the condition of the self-adjoint and the non-self-adjoint, also look for the formation or non-formation of boundary layers for local boundary conditions using the Frequent uniform limit method. Also, for the state of non-local conditions, we convert the non-local boundary conditions into local conditions by finding the fundamental solution and then obtaining the necessary conditions with the help of the 4-step method. Finally, we determine the formation or non-formation of a boundary layer for non-local conditions such as local conditions.On 1-index of Unstable Spacelike Hypersurfaces in Pseudo-Euclidean Spheres
https://scma.maragheh.ac.ir/article_248103.html
In mathematical physics, the stable hypersurfaces of constant mean curvature in pseudo-Euclidian spheres have been interested by many researchers on general relativity. As an extension, the notion of index of stability has been introduced for unstable ones. The stability index (as a rate of distance from being stable) is defined in terms of the Laplace operator $\Delta$ as the trace of Hessian tensor. In this paper, we study an extension of stability index(namely, 1-index) of hypersurfaces with constant scalar curvature in pseudo-Euclidian sphere $\S_1^{n+1}$. 1-index is defined based on the Cheng-Yau operator $\Box$ as a natural extension of $\Delta$.On Approximating Fixed Point in CAT(0) Spaces
https://scma.maragheh.ac.ir/article_246179.html
In this paper, we obtain a new modified iteration process in the setting of CAT(0) spaces involving generalized $\alpha$-nonexpansive mapping. We prove strong and $\Delta$ convergence results for approximating fixed point via newly defined iteration process. Further, we reconfirm our results by non trivial example and tables.An 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.