Approximation by Jackson-type operator on the sphere

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.