On the approximation properties of Cesàro means of negative order of double Vilenkin – Fourier series

T.  Tepnadze

doi:10.37863/umzh.v72i3.6045

T. Tepnadze I. Javakhishvili Tbilisi State Univ., Georgia

DOI: https://doi.org/10.37863/umzh.v72i3.6045

Abstract

UDC 517.5

We establish approximation properties of Ces\`{a}ro $% (C,-\alpha ,-\beta)$ 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.

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