Surveys in Mathematics and its Applications

ISSN1842-6298 (electronic), 1843-7265 (print)

Volume 5 (2010), 113 -- 122## DEGREE OF APPROXIMATION OF FUNCTIONS BELONGING TO LIPα CLASS AND WEIGHTED (L

^{r},ξ(t)) CLASS BY PRODUCT SUMMABILITY METHOD## Hare Krishna Nigam

Abstract. A good amount of work has been done on degree of approximation of functions belonging to Lipα, Lip(α,r), Lip(ξ(t),r) and W(L^{r}, ξ(t)) classes using Cesàro and (generalized) Nörlund single summability methods by a number of researchers like Alexits [1], Sahney and Goel [11], Qureshi and Neha [9], Quershi [7, 8], Chandra [2], Khan [4], Leindler [5] and Rhoades [10]. But till now no work seems to have been done so far in the direction of present work. Therefore, in present paper, two quite new results on degree of approximation of functions f∈ Lipα and f∈ W(L^{r},ξ(t)) class by (E,1)(C,1) product summability means of Fourier series have been obtained.2010 Mathematics Subject Classification:42B05, 42B08.

Keywords:Degree of approximation; Lipα class; W(L^{r},ξ(t)) class of functions; (E,1) means; (C,1) means; (E,1)(C,1) product means; Fourier series; Lebesgue integral.

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Hare Krishna Nigam

Department of Mathematics,

Faculty of Engineering and Technology,

Mody Institute of Technology and Science (Deemed University)

Laxmangarh, Sikar-332311,

Rajasthan, India.

e-mail: harekrishnan@yahoo.com