Sahand Communications in Mathematical Analysis
Volume:18 Issue: 4, Autumn 2021

We study the concept of frame in tensor product of  $n$-Hilbert spaces as tensor product of  $n$-Hilbert spaces is again an  $n$-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  $n$-Hilbert spaces is studied. Finally,;the dual frame in tensor product of  $n$-Hilbert spaces is discussed.

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.

In this paper,  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.

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.

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 $L_m,, mgeq 1$ norm of differentiable functions. Also, we give some applications of the probability density function.

‎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.

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 $Delta$.

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.