Abstract

Statistical convergence is more extensive than the classical convergence and has recently drawn the recognition of many researchers. The Korovkin-type approximation theorems are usually based on the convergence analysis of sequences of positive linear operators. Gradually, such approximation theorems are extended over more general sequence spaces with several settings via different kinds of statistical summability techniques. In this paper, we introduce presumably a new statistical Riesz-Euler product summability technique to prove a Korovkin-type approximation theorem. Moreover, we demonstrate another result for the rate of statistical convergence under our proposed summability technique.

Keywords and Phrases

Statistical convergence; Korovkin's theorem; positive linear operator; $(E,q)$ mean; $(\overline{N},p_{n},q_{n})$ mean.

A.M.S. subject classification

41A24, 41A25, 42B05, 42B08.

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