IJPAM: Volume 70, No. 6 (2011)

DEGREE OF APPROXIMATION OF
A FUNCTION BELONGING TO $Lip\left( \xi(t), r \right)$
CLASS BY $(E,1)(C,1)$ PRODUCT MEANS

Hare Krishna Nigam$^1$, Kusum 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, a new theorem on degree of approximation of a function belonging to $Lip \left( \xi\left( t \right),r \right)$ class by $(E,1)(C,1)$ product summability means of its Fourier series has been obtained.

Received: December 23, 2010

AMS Subject Classification: 42B05, 42B08

Key Words and Phrases: degree of approximation, \(W\left( L_{r},\xi\left( t \right) \right)\) class of function, $(C,1)$ 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: 2011
Volume: 70
Issue: 6