Approximation properties of convolution operators via statistical convergence based on a power series

Year 2025, Volume: 74 Issue: 1, 92 - 102

Ramazan Dinar , Tuğba Yurdakadim

Abstract

In this study, our main goal is to obtain approximation properties of convolution operators for multivariables via a special method which is not included in any other methods given before, also known as $P$-statistical convergence. We present the $P$-statistical rate of this approximation and provide examples of convolution operators. It is noteworthy to express that one can not approximate $f$ by earlier results for our examples. Therefore, our results fill an important gap in the existing literature. Furthermore, we also present a $P$-statistical approximation result in the space of periodic continuous functions of period $2\pi$ for short $C^*$.

Keywords

Power series method, statistical convergence, convolution operators, Korovkin type approximation, rate of convergence

Ethical Statement

The authors declare that there are no competing interests.

Supporting Institution

There is no funding.

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