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

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

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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Published
28.03.2020
How to Cite
Tepnadze, T. “On the Approximation Properties of Cesàro Means of Negative Order of Double Vilenkin – Fourier Series”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 3, Mar. 2020, pp. 391-06, doi:10.37863/umzh.v72i3.6045.
Section
Research articles