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

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 $C^*$.