Summability Results for Infinite and Fourier Series

Abstract

In this study, a theorem related to a general summability method is proved. The purpose of the paper is to investigate the fundamental properties of this method and to determine conditions under which it can be effectively applied to series that are not convergent in the usual sense. The results obtained provide a broader perspective on summability theory and extend several known results in the literature. As an application of the established theorem, a result concerning the summability of trigonometric Fourier series is derived. In particular, sufficient conditions ensuring the summability of Fourier series are discussed. The findings of this paper contribute to the summability theory of infinite series and demonstrate the usefulness of the proposed method in Fourier analysis.