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 article we introduce approximation spaces for parabolic problems which are based on the tensor product construction of a multiscale basis in space and a multiscale basis in time. Proper truncation then leads to so-called space-time sparse grid spaces. For a uniform discretization of the spatial space of dimension d with O(N) degrees of freedom, these spaces involve for d > 1 also only O...

in this letter, the numerical scheme of nonlinear volterra-fredholm integro-differential equations is proposed in a reproducing kernel hilbert space (rkhs). the method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satis ed. the nonlinear terms are replaced by its taylor series. in this technique, the nonlinear volterra-fredholm integr...

Let {φk}1 be a frame for Hilbert space H. The purpose of this paper is to present an approximation formula of any f ∈ H by a linear combination of finitely many frame elements in the frame {φk}1 and show that the obtained approximation error depends on the bounds of frame and the convergence rate of frame coefficients of f as well as the relation among frame elements.

This paper is devoted to a nearness relation in an Efremovic̆proximity space. The basic approach is to consider the nearness of the upper and lower approximation of a set introduced by Z. Pawlak during the early 1980s as a foundation for rough sets. Two forms of nearness relations are considered, namely, a spatial EFand a descriptive EFrelation. This leads to a study of the nearness of objects e...

Multigranulation rough set theory is a relatively new mathematical tool for solving complex problems in the multigranulation or distributed circumstances which are characterized by vagueness and uncertainty. In this paper, we first introduce the multigranulation approximation space. According to the idea of fusing uncertain, imprecise information, we then present three uncertainty measures: fus...

The phase transition between solid and liquid in an undercooled liquid leads to dendritic growth of the solid phase. The problem is modelled by the Stefan problem with a modiied Gibbs-Thomson law, which includes the anisotropic mean curvature corresponding to a surface energy that depends on the direction of the interface normal. A nite element method for discretization of the Stefan problem is...