On Approximation of Functions Belonging to Lip(α, r) Class and to Weighted W(Lr,ξ(t)) Class by Product Mean

• Journal title : Kyungpook mathematical journal
• Volume 50, Issue 4,  2010, pp.545-556
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2010.50.4.545
Title & Authors
On Approximation of Functions Belonging to Lip(α, r) Class and to Weighted W(Lr,ξ(t)) Class by Product Mean
Nigam, Hare Krishna; Sharm, Ajay;

Abstract
A good amount of work has been done on degree of approximation of functions belonging to Lip$\small{{\alpha}}$, Lip($\small{\xi}$(t),r) and W($\small{L_r,\xi(t)}$) and classes using Ces$\small{\`{a}}$ro, N$\small{\"{o}}$rlund and generalised N$\small{\"{o}}$rlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,$\small{p_n}$)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function $\small{f\;\in\;Lip({\alpha},r)}$ class and $\small{f\;\in\;W(L_r,\;\xi(t))}$ class by (N, $\small{p_n}$)(C, 1) product summability means of its Fourier series.
Keywords
Degree of approximation;Lip($\small{{\alpha}}$, r) class;$\small{W(L_r,\\xi(t))}$ class functions;(N, $\small{p_n}$) mean;(C,1) mean;(N, $\small{p_n}$)(C, 1) product means;Fourier series;Lebesgue integral;
Language
English
Cited by
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