Surveys in Mathematics and its Applications

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

Volume 8 (2013), 125-- 136## ON APPROXIMATION OF FUNCTIONS BY PRODUCT OPERATORS

## Hare Krishna Nigam

Abstract. In the present paper, two quite new reults on the degree of approximation of a function f belonging to the class Lip(α,r), 1≤ r <∞ and the weighted class W(L_{r},ξ(t)), 1≤ r <∞ by (C,2)(E,1) product operators have been obtained. The results obtained in the present paper generalize various known results on single operators.2010 Mathematics Subject Classification:Primary 42B05, 42B08.

Keywords:Degree of approximation; Function of class Lip(α,r); Function of class W(L_{r},ξ(t)); (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