Abstract
In this paper, we obtain a Korovkin type approximation result for a sequence of positive linear operators defined on modular spaces with the use of power series method . We also provide an example which satisfies our theorem.
Highlights
The classical Korovkin theorem states the uniform convergence of a sequence of positive linear operators in C[a; b], the space of all continuous real valued functions de...ned on [a; b] by providing the convergence only on three test functions f1; x; x2g
Some versions of Korovkin type theorems have been given in modular spaces that include as particular cases Lp, Orlicz and Musielak-Orlicz spaces [8, 19] with the use of more general convergences such as convergences generated by summability methods, statistical, ...lter convergence [9, 10, 11, 14, 15, 16, 20]
We give a Korovkin type theorem in modular spaces by power series method which includes both Abel and Borel methods
Summary
The classical Korovkin theorem states the uniform convergence of a sequence of positive linear operators in C[a; b], the space of all continuous real valued functions de...ned on [a; b] by providing the convergence only on three test functions f1; x; x2g. There are trigonometric versions of this theorem with the test functions f1; cos x; sin xg and abstract Korovkin type results have been studied [13, 17]. These type of results let us to say the convergence with minimum calculations and have important applications in the polynomial approximation theory, in various areas of functional analysis, in numerical solutions of di¤erential and integral equations [1, 2]. We give a Korovkin type theorem in modular spaces by power series method which includes both Abel and Borel methods.
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