ON APPROXIMATION OF CONTINUOUS FUNCTION IN THE HöLDER METRIC BY ( C, 1)[F, d_n] MEANS OF ITS FOURIER SERIES

By

H. L. Rathore¹, U. K. Shrivastava² and Lakshmi Narayan Mishra³

¹Department of Mathematics, Government College Pendra, Bilaspur- 495119, Chhattisgarh, India

Corresponding author:hemlalrathore@gmail.com

²Department of Mathematics, Government E.R. Rao Science PG College, Bilaspur – 495001, Chhattisgarh, India

Email:profumesh18@yahoo.co.in

³Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT), University, Vellore- 632014, Tamil Nadu, India Email:lakshminarayanmishra04@gmail.com

(Received: August 01, 2021; In format : August 27, 2021; Revised in final form : October 23, 2021)

DOI: https://doi.org/10.58250/Jnanabha.2021.51219

Abstract

In the present paper we determine a new estimate for the [F, d_n] matrix method which is introduced by Jakimovsky (1959) as generalization of both the Euler E_r method and Stirling-Karamata-Lototsky method. Further we extend the under weaker condition of Hölder metric using Cesro mean and [F, d_n] mean the associate with Fourier series. We obtained a theorem on approximation of continuous function in the Hölder metric by (C, 1)[F, d_n] means of its Fourier series.

2020 Mathematical Sciences Classification: 42B05, 42B08

Keywords and Phrases: Holder metric, Fourier series, Banach Spaces, Degree of approximation, ( C, 1)[F, d_n] method, (C, 1) mean.

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