ON THE DEGREE OF APPROXIMATION OF FUNCTION ƒ ∈ W (Lp, ζ(t)) CLASS BY (C, 2)(e, c) MEANS OF ITS FOURIER SERIES
By
H. L. Rathore
Department of Mathematics, Government College Pendra, Bilaspur, Chhattisgarh, India-495119.
Email: hemlalrathore@gmail.com
(Received: May 22, 2023; In format : May 25, 2023; Revised: October 26, 2023; Accepted: October 30, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53224
Abstract
We study on degree of approximation of function belonging to weighted (Lp, ζ(t)) class by (C; 1)(e, c) mean and weighted (Lp, ζ(t)) class by (C, 2)(E, q) has been discussed by Rathore and Shrivastava. Since (e, c) includes (E; q) method, so for obtaining more generalized result we replace (E, q) by (e, c) mean. Which is a regular method of summation for c > 0. In this paper we obtain the degree of approximation of the function belonging to weighted (Lp, ζ(t)) class by (C, 2)(e, c) product means of its Fourier series has been proved.
2020 Mathematical Sciences Classification: 42B05, 42B08.
Keywords and Phrases: Degree of approximation, W (Lp, ζ(t)) class of function, (C; 2) summability, (e, c) summability, (C, 2)(e, c) product summability, Fourier series, Lebesgue integral.