IJPAM: Volume 78, No. 5 (2012)

A NEW METHOD $(E,q)(C,1)$ OF SUMMATION AND
DEGREE OF APPROXIMATION OF THE FUNCTIONS
IN GENERALIZED $L^r-$NORM

Shyam Lal$^1$, Abhishek Mishra$^2$
$^{1,2}$Department of Mathematics
Faculty of Science
Banaras Hindu University
Varanasi, INDIA


Abstract. In this paper, new estimates on the degree of approximation of a function $f$ belonging to $Lip(\alpha,r)$ $(r\geq1)$ and $Lip(\xi,r)$ $(r\geq1)$, by $(E,q)(C,1)$ summability means of its Fourier Series have been established.

Received: December 20, 2011

AMS Subject Classification: 42B05, 42B08

Key Words and Phrases: trigonometric approximation, Fourier series, $(C,1)$ means, $(E,q)$ means, and $(E,q)(C,1)$ summability means, generalized Minkowski's inequality

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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: 78
Issue: 5