IJPAM: Volume 82, No. 3 (2013)

ON (E,1)(C,1) SUMMABILITY OF
FOURIER SERIES AND ITS CONJUGATE SERIES

Hare Krishna Nigam$^1$, Kusum Sharma$^2$
Department of Mathematics
Faculty of Engineering and Technology
Mody Institute of Technology and Science (Deemed University)
Laxmangarh, 332311, Sikar, Rajasthan, INDIA


Abstract. Several researchers like Singh [7], Khare [3], Mittal and Kumar [5], singh and singh [8], Pandey [6] and Jadia [2] have studied \(\left(N,p_{n}\right),\left( N,p,q \right)\), almost \(\left(N,p,q\right)\) and matrix summability methods of Fourier series and its conjugate series using different conditions. But nothing seems to have been done so far to study $(E,1)(C,1)$ product summability of Fourier series and its conjugate series. Therefore, in this paper, two theorems on ${(E,1)(C,1)}$ summability of Fourier series and its conjugate series under a general condition have been proved.

Received: June 5, 2012

AMS Subject Classification: 42B05, 42B08

Key Words and Phrases: degree of approximation, $(C,1)$ summability, \(\left(E,1\right)\) summability, \(\left(C,1\right)\left( E,1\right)\) product summability, 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
Year: 2013
Volume: 82
Issue: 3