On the Approximation Properties of Cesàro Means of Negative Order of double Vilenkin-Fourier Series

Abstract

In this paper we establish approximation properties of Cesàro means with $\alpha ,\beta$ $\epsilon$ $(0,1)$ of Vilenkin-Fourier series.This result allows one to obtain a condition which is sufficient for the convergence of the means ${\sigma }_{n,m}^{-\alpha ,-\beta }(x,y,f)$ to $f(x,y)$ in the $L^p-$metric.

arXiv admin note: substantial text overlap with arXiv:1811.07704; text overlap with arXiv:1609.01646, arXiv:1609.01642 by other authors