arXiv subjects
Publications and source records attributed to Tsitsino Tepnadze.
In this paper we state and prove some new inequalities related to the rate of $L^{p}$ approximation by Cesàro means of the quadratic partial sums of double Vilenkin-Fourier series of functions from $L^{p}$.
In this paper we establish approximation properties of Cesàro $(C,-α)$ means with $α$ $ε$ $(0,1)$ of Vilenkin-Fourier series.This result allows one to obtain a condition which is sufficient for the convergence of the means $σ_n^{-α}(f,x)$ to $f(x)$ in the $L^p-$metric.
In this paper we establish approximation properties of Cesàro $% (C,-α,-β)$ means with $α,β$ $ε$ $(0,1)$ of Vilenkin-Fourier series.This result allows one to obtain a condition which is sufficient for the convergence of the means $σ_{n,m}^{-α,-β}(x,y,f)$ to $f(x,y)$ in the $L^{p}-$metric.