On T-Strong Convergence of Numerical Sequences and Fourier Series

Abstract

In this paper, we generalize the notion of \(\varLambda \)-strong convergence of numerical sequences defined by Moricz (Acta Math Hung 54(3–4):319–327, 1989) to T-strong convergence, using a lower triangular matrix \(T=(a_{n,k})\) with nondecreasing monotone rows of positive numbers tending to \(\infty \) i.e., \(a_{n,k}\le a_{n,k+1} \forall n\) and \(\lim _{k\rightarrow \infty } a_{n,k}=\infty \,\, \forall n\). We also establish a relationship between ordinary convergence and T-strong convergence. We further show that this concept can also be applied to the strong convergence of Fourier series under C-metric and \(L_{p}\)-metric.