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.