Surveys in Mathematics and its Applications


ISSN 1842-6298 (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(Lr,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(Lr,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

http://www.utgjiu.ro/math/sma