ON APPROXIMATION OF CONTINUOUS FUNCTION IN THE HöLDER METRIC BY ( C, 1)[F, dn] MEANS OF ITS FOURIER SERIES
H. L. Rathore1, U. K. Shrivastava2 and Lakshmi Narayan Mishra3
1Department of Mathematics, Government College Pendra, Bilaspur- 495119, Chhattisgarh, India
2Department of Mathematics, Government E.R. Rao Science PG College, Bilaspur – 495001, Chhattisgarh, India
3Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT), University, Vellore- 632014, Tamil Nadu, India Email:email@example.com
(Received: August 01, 2021; In format : August 27, 2021; Revised in final form : October 23, 2021)
In the present paper we determine a new estimate for the [F, dn] matrix method which is introduced by Jakimovsky (1959) as generalization of both the Euler Er method and Stirling-Karamata-Lototsky method. Further we extend the under weaker condition of Hölder metric using Cesro mean and [F, dn] mean the associate with Fourier series. We obtained a theorem on approximation of continuous function in the Hölder metric by (C, 1)[F, dn] 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, dn] method, (C, 1) mean.
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