International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 298923, 13 pages
http://dx.doi.org/10.1155/2012/298923
Research Article

Product Summability Transform of Conjugate Series of Fourier Series

Vishnu Narayan Mishra,1 Kejal Khatri,1 and Lakshmi Narayan Mishra2

1Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Road, Surat 395 007, India
2Dr. Ram Manohar Lohia Avadh University, Hawai Patti Allahabad Road, Faizabad 224 001, India

Received 22 February 2012; Revised 15 March 2012; Accepted 15 March 2012

Academic Editor: Ram U. Verma

Copyright © 2012 Vishnu Narayan Mishra et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A known theorem, Nigam (2010) dealing with the degree of approximation of conjugate of a signal belonging to L i p 𝜉 ( 𝑡 ) -class by ( 𝐸 , 1 ) ( 𝐶 , 1 ) product summability means of conjugate series of Fourier series has been generalized for the weighted 𝑊 ( 𝐿 𝑟 , 𝜉 ( 𝑡 ) ) , ( 𝑟 ≥ 1 ) , ( 𝑡 > 0 ) -class, where 𝜉 ( 𝑡 ) is nonnegative and increasing function of 𝑡 , by 𝐸 1 𝑛 𝐶 1 𝑛 which is in more general form of Theorem 2 of Nigam and Sharma (2011).