A Korovkin theorem in multivariate modular function spaces

Matrix Summability and Korovkin Type Approximation Theorem on Modular Spaces

In this paper, using a matrix summability method we obtain a Korovkin type approximation theorem for a sequence of positive linear operators defined on a modular space.

Abstract Korovkin-type theorems in modular spaces and applications

Korovkin-type theorems in modular spaces and applications C. Bardaro ∗ A. Boccuto † X. Dimitriou ‡ I. Mantellini § Abstract We prove some versions of abstract Korovkin-type theorems in modular function spaces, with respect to filter convergence for linear positive operators, by considering several kinds of test functions. We give some results even with respect to an axiomatic convergence, whose...

Quantitative Multivariate Random Korovkin Theory

We introduce and study the very general multivariate stochastic positive linear operators induced by general multivariate positive linear operators that are acting on multivariate continuous functions. These are acting on the spaces of real differentiable multivariate time stochastic processes. Under some very mild, general and natural assumptions on the stochastic processes we produce related ...

Variations on a Theorem of Korovkin

A Fixed Point Theorem and Its Application to Integral Equations in Modular Function Spaces

In this paper we present a fixed point theorem of Banach type in modular space. We give an application of this result to a nonlinear integral equation in Musielak-Orlicz space. 0. Introduction It is well known that one of the standard proofs of Banach’s fixed point theorem is based on Cantor’s theorem in complete metric spaces [3, 4]. To this end, using some convenient constants in the contract...