On $\Lambda^{r}$-strong convergence of numerical sequences and Fourier series

TL;DR

This paper investigates $oldsymbol{ extLambda^{r}}$-strong convergence, extending previous results to provide new theorems on the convergence behavior of numerical sequences and Fourier series.

Contribution

It introduces new theorems on $oldsymbol{ extLambda^{r}}$-strong convergence, expanding the existing theoretical framework and extending prior results by Móricz.

Findings

New theorems on $oldsymbol{ extLambda^{r}}$-strong convergence

Extended results on Fourier series convergence

Broadened understanding of numerical sequence convergence

Abstract

We prove theorems of interest about the recently given $\Lambda^{r}$-strong convergence. We extend the results of F. M\'oricz [On $\Lambda$-strong convergence of numerical sequences and Fourier series, Acta Math.~Hungar., 54 (1989), 319--327].