IJPAM: Volume 76, No. 2 (2012)

ON APPROXIMATION OF CONJUGATE OF FUNCTIONS
BELONGING TO DIFFERENT CLASSES
BY PRODUCT MEANS

H.K. Nigam$^1$, Ajay Sharma$^2$
$^{1,2}$Department of Mathematics
Faculty of Engineering and Technology
Mody Institute of Technology and Science (Deemed University)
Laxmangarh, 332311, Sikar (Rajasthan), INDIA


Abstract. In this paper, we introduce the concept of (C,1)(E,q) product summability and establish a quite new theorem on degree of approximation of conjugate of the function $ f \in W\left( {{L_r},\xi \left( t \right)} \right)$ class by (C,1)(E,q) product summability means of conjugate Fourier series.

Received: March 10, 2012

AMS Subject Classification: 42B05, 42B08

Key Words and Phrases: degree of approximation, $W\left( {{L_r},\xi \left( t \right)} \right)$ class of functions, $(C,1)$ summability, $(E,q) $ summability, $(C,1)(E,q)$ product summability, 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
Year: 2012
Volume: 76
Issue: 2