ON THE DEGREE OF APPROXIMATION OF FUNCTIONS BELONGING TO THE LIPSCHITZ CLASS BY $(e,c)$ MEANS

Abstract


 
 
 In the present paper, we obtain the degree of approximation of $f\in$ Lip$\alpha$ ($0 <\alpha\le 1$) by ($e, c$) means ($c > 0$) of its Fourier Series. 
 
 

ON THE DEGREE OF APPROXIMATION OF FUNCTION ƒ ∈ W (Lp, ζ(t)) CLASS BY (C, 2)(e, c) MEANS OF ITS FOURIER SERIES

“…The inequality (3.2) follows from (3.1). (3.3) may be obtained by using Able's Lemma and (3.4) may be obtained by classical formula for theta function by Siddiqui [18] and (3.1) is due to Shrivastava & Verma [19].…”

“…We study on approximation of f belonging to many classes. Also W (L p , (ξ(t)) by Cesǎro mean, Nörlund mean, has been discussed by several researchers like Alexits [1], Khan [6], Chandra [3], Sahney and Goel [17], Quereshi [12], Shrivastava and Verma [19], Mishra et al [10] etc. Rathore and Shrivastava [13] extended the result on degree of approximation of a function belonging to W (L r , ξ(t)) class by (C, 1)(e, c) means of Fourier series.…”

“…Further Rathore and Shrivastava [14] studied about product summability on approximation of a function belonging to W (L r , ξ(t)) class by (C, 2) (E, q) means. In this direction several researchers like Lal and Singh [9], Lal and Kushwaha [8], Nigam [11], Albayrak, Koklu and Bayramov [2], Rathore, Shrivastava and Mishra ( [15], [16]) etc. Recently Kushwaha [7] has determined on approximation of function by (C, 2)(E, 1) product summability method of Fourier series, but till now no work done to extend the result on approximation of function f W (L p , ξ(t)) class by (C, 2)(e, c) mean has been seen.…”