Degree of approximation of the conjugate of signals (functions) belonging to Lip ( α , r ) -class by ( C , 1 ) ( E , q ) means of conjugate trigonometric Fourier series

Abstract

In this paper, we determine the degree of approximation of the conjugate of

A Study on Approximation of a Conjugate Function Using Cesàro-Matrix Product Operator

“…Our theorems generalizes six previously known results. Thus, the results of [5,[8][9][10][11][12] becomes the special cases of our theorem. Some inportant corollaries are also obtained from our theorems.…”

“…6.1. If we take Remark 1 iv ðÞ and β ¼ 0, ξω ðÞ ¼ ω α ,0< α ≤ 1 in our theorem, then the Theorem 2 of [8] become a special case of our theorem.…”

“…of the CFS is given by (8) and ξω ðÞ satisfies the conditions (21) to (24). Corollary 5.9 The error estimate of ζ ∈ WL p , ξω ðÞ ðÞ class by C δ E 1 means…”

“…of the FS is given by (8) and ξω ðÞ satisfies the conditions (21) to (24). Remark 6 The corollaries for 5.1 to 5.9 can also be obtained for the special cases C 1 H, C 1 N p ,C 1 N pq ,C 1 Ñp , C 1 E q and C 1 E 1 all things considered Remark 3.…”

“…in past few decades. The studies of estimation of error of cojugate of functions in different Lipschitz classes and Hölder classes using different product operator, have been made by the researchers like [5][6][7][8][9][10][11][12] etc. in recent past.…”