IJPAM: Volume 70, No. 3 (2011)
BELONGING TO WEIGHTED
CLASS BY PRODUCT MEANS
Department of Mathematics
Faculty of Engineering and Technology
Mody Institute of Technology and Science (Deemed University)
Laxmangarh, 332311, Sikar (Rajasthan), INDIA
Abstract. A good amount of work has been done on degree of approximation of functions belonging to and classes using Cesro, Nrlund and generalised Nrlund single summability methods by a number of researchers (see [#!ga!#], [#!pc!#], [#!hk!#], [#!ll!#], [#!kq1!#], [#!kq2!#], [#!qn!#], [#!br!#], [#!sg!#]). But till now, nothing seems to have been done so far to obtain the degree of approximation of conjugate of a function using product summability method of its conjugate Fourier series. Therefore, the purpose of present paper is to establish a quite new theorem on degree of approximation of a function , conjugate to a periodic function belonging to weighted, i.e. class, , by product summability means of its conjugate Fourier series.
Received: December 28, 2010
AMS Subject Classification: 42B05, 42B08
Key Words and Phrases: degree of approximation, class of function, mean, mean, product means, Fourier series, conjugate Fourier series, Lebesgue integral
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395