Original scientific paper

Approximation by Jackson-type operator on the sphere

Feilong Cao ; Department of Information and Mathematics Sciences, China Jiliang University, Hangzhou, P.R. China
Xiaofei Guo ; Department of Information and Mathematics Sciences, China Jiliang University, Hangzhou, P.R. China

Abstract

This paper discusses the approximation by a Jackson-type operator on the sphere. By using a spherical translation operator, a modulus of smoothness of high order, which is used to bound the rate of approximation of the Jackson-type operator, is introduced.
Furthermore, the method of multipliers is applied to characterize the saturation order and saturation class of the operator. In particular, the function of saturation class is expressed by an apparent formula. The results obtained in this paper contain the corresponding
ones of the Jackson operator.

Keywords

approximation; Jackson-type operator; saturation order; saturation class; sphere

Hrčak ID:

61810

URI

https://hrcak.srce.hr/61810

Publication date:

8.12.2010.

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