On strong summability of the Fourier series via deferred Riesz mean

J. Sahoo ; B. B. Jena ; S. K. Paikray

Problemy analiza, Tome 13 (2024) no. 2, pp. 128-143

Résumé

The strong summability technique has attracted a remarkably large number of researchers for better convergence analysis of infinite series as well as Fourier series in the study of summability theory. The of strong summability method was introduced by Fekete (Math. És Termesz Ertesitö, 34 (1916), 759–786). In this paper, we introduce the notions of strong deferred Cesàro, deferred Nörlund, and deferred Riesz summability methods. We then consider our proposed strong deferred Riesz summability mean to establish and prove a new theorem for the summability of the Fourier series of an arbitrary periodic function. Moreover, for the effectiveness of our study, we present some concluding remarks demonstrating that some earlier published results are recovered from our main non-trivial Theorem.

Détail

Keywords: strong summability, deferred Cesàro summability, $[D\bar{N}, 2]$-summability, arbitrary periodic function, Fourier series.
Mots-clés : p_{n}^{(1)}