In this article to prove existence of solution of infinite system of nonlinear integral equations, we consider the space of solution containing all convergence sequences with a finite limit, as with a suitable norm is a Banach space. By creating a generalization of Meir-Keeler condensing operators which is named as F-generalized Meir-Keeler condensing operators and measure of noncompactness, we...

In this paper we extend the definition of generalized Sobolev space and subsequent theoretical results established recently for positive definite kernels and differential operators in the article [21]. In the present paper the semi-inner product of the generalized Sobolev space is set up by a vector distributional operator P consisting of finitely or countably many distributional operators Pn, ...

In many applications, one deals with nonsmooth functions, e.g., in dynamical systems, mechanics, or optimization. order to establish theoretical results, it is often beneficial regularize the functions an intermediate step. this work, we investigate properties of a generalization Moreau–Yosida regularization on normed space where replace quadratic kernel infimal convolution more general functio...

in this paper, we introduce a new type of almost statistical convergence of generalized difference sequences of fuzzy numbers. we give the relations between the strongly almost cesàro type convergence and almost statistical convergence in these spaces. furthermore, we study some of their properties like completeness, solidity, symmetricity etc. we also give some inclusion relations related to t...

The paper deals with finding criteria for the Hausdorff convergence of sequences of convolution operators on quasi-Banach spaces of periodic realvalued distributions (generalized functions). In particular, the criteria for convergence on the Hardy classes, on the class of regular Borel measures, and on the class of pseudomeasures are found. These assertions are special cases of the general resu...

‎Let $X,Y$ be normed spaces with $L(X,Y)$ the space of continuous‎ ‎linear operators from $X$ into $Y$‎. ‎If ${T_{j}}$ is a sequence in $L(X,Y)$,‎ ‎the (bounded) multiplier space for the series $sum T_{j}$ is defined to be‎ [ ‎M^{infty}(sum T_{j})={{x_{j}}in l^{infty}(X):sum_{j=1}^{infty}%‎ ‎T_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $S:M^{infty}(sum T_{j})rightarrow Y$ associat...

Coarse spaces are instrumental in obtaining scalability for domain decomposition methods. However, it is known that most popular choices of coarse spaces perform rather weakly in presence of heterogeneities in the coefficients in the partial differential equations, especially for systems. Here, we introduce in a variational setting a new coarse space that is robust even when there are such hete...

We introduce a universal and systematic way of defining a generalized Bspline based on a linear shift-invariant (LSI) operator L (a.k.a. Fourier multiplier). The generic form of the B-spline is βL = LdL −1δ where L−1δ is the Green’s function of L and where Ld is the discretized version of the operator that has the smallest-possible null space. The cornerstone of our approach is a main construct...