On the Approximation Properties of Cesàro Means of Negative Order for the Double Vilenkin–Fourier Series

Abstract

We establish approximation properties of Cesaro (C,−α,−β) means with α, β 𝜖 (0, 1) for the Vilenkin–Fourier series. This result enables one to establish a condition sufficient for the convergence of the means $$ {\sigma}_{n,m}^{-\alpha, -\beta } $$ (x, y, f) to f(x, y) in the Lp-metric.