On strong summability of the Fourier series via deferred Riesz mean

J. Sahoo^a, B. B. Jena^b, S. K. Paikray<sup>a

a</sup> Department of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, Odisha, India
^b Faculty of Science (Mathematics), Sri Sri University, Cuttack 754006, Odisha, India

Abstract: 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.

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

UDC: 517.521

MSC: 30D40

Received: 21.11.2023
Revised: 10.05.2024
Accepted: 14.05.2024

Language: English

DOI: 10.15393/j3.art.2024.15090