Approximation of Functions by (C~1.T)means of its Fourier-Laguerre series

摘要

In 1971, Gupta [1] estimated the order of the function by Cesaro means of Fourier - Laguerre series at the point x = 0, after replacing the continuity condition in Szego's theorem [8]. In continuation Singh [7] estimated the degree of approximation at the pointx = 0, by some weaker conditions than Gupta [1]. Nigam and Sharma [5], [6] proved a theorem of such type using (E, 1), (N, p, q)(E,1)means which is entirely different from (C, k) and harmonic means of the Fourier - Laguerre series. They employed a condition which is weaker than Singh [7] and also increased the range of α to (-1, -1/2) which is more appropriate for applications. Very recently, Krasniqi [3] has proved one theorem on the degree of approximation of a function by (C, 1)(E, q) means of its Fourier-Laguerre. In this paper we prove a theorem on the degree of approximation of a function by (C~1.T)means of its Fourier-Laguerre series at the frontier point x = 0.