A new study on the absolute matrix summability of non-decreasing sequences

TL;DR

This paper generalizes a recent theorem on absolute matrix summability factors of series by extending it from weighted mean matrices to normal matrices, broadening the scope of summability methods.

Contribution

It introduces a generalized theorem for $|A, p_{n}|_{k}$ summability using normal matrices, expanding previous results on summability factors.

Findings

Generalization of Bor's theorem to normal matrices

Broader applicability of summability factor results

Enhanced understanding of matrix summability methods

Abstract

Recently, in [Bor4], Bor proved a main theorem dealing with $|\bar{N}, p_{n}|_{k}$ summability factors of infinite series. In the present paper, we have generalized that theorem for $|A, p_{n}|_{k}$ summability method by taking normal matrices in place of weighted mean matrices.