APPROXIMATION OF FUNCTIONS IN THE GENERALIZED ZYGMUND CLASS USING PRODUCT MEANS OF DERIVED FOURIER SERIES


By

Aradhana Dutt Jauhari¹ and Santosh Kumar² 

¹Division of Mathematics, School of Basic Sciences, Galgotias University, Greater Noida, Gautam Buddha Nagar, Uttar Pradesh, India-203201 ²Department of Mathematics, School of Physical Sciences, North Eastern Hill University, Shillong, Meghalaya, India-793022 

Email: draradhana27@gmail.com, drsengar2002@gmail.com 

(Received: April 20, 2024; In format: April 30, 2024; Revised: June 05, 2024; Accepted: June 10, 2024) 


DOI: https://doi.org/10.58250/jnanabha.2024.54136 



Abstract

In this paper, we investigate the potential of using the product means of the derived Fourier series to approximate functions within the generalized Zygmund class. The product means offer a flexible and powerful tool for approximation due to their ability to capture intricate local behaviors of functions. We establish convergence theorems for the product means of the derived Fourier series, providing conditions under which these approximations converge uniformly to the original function in the generalized Zygmund class. 


2020 Mathematical Sciences Classification: 41A10, 41A25, 42B05, 42A50, 40G05. 

Keywords and Phrases: Fourier Series, Derived Fourier Series, Matrix (∆) means, Matrix-Euler (∆Eq) means, Generalised Zygmund Class. 

[Download PDF File]