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Approximation by Generalized Kantorovich Sampling Type Series

Angamuthu Sathish Kumar|Ponnaian Devaraj
경북대학교 자연과학대학 수학과|2019.09|Kyungpook Mathematical Journal|제59권 제3호|pp. 465-480|DOI 10.5666/KMJ.2019.59.3.465

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참고문헌

키워드

rate of convergencesampling Kantorovich operatorsVoronovskaya type formulamodulus of smoothness
주제분류수학

초록

In the present article, we analyse the behaviour of a new family of Kantorovich type sampling operators (Kφ wf)w>0: First, we give a Voronovskaya type theorem for these Kantorovich generalized sampling series and a corresponding quantitative version in terms of the rst order of modulus of continuity. Further, we study the order of approximation in C(R), the set of all uniformly continuous and bounded functions on R for the family (Kφ wf)w>0. Finally, we give some examples of kernels such as B-spline kernels and the Blackman-Harris kernel to which the theory can be applied.

Abstract

In the present article, we analyse the behaviour of a new family of Kantorovich type sampling operators (Kφ wf)w>0: First, we give a Voronovskaya type theorem for these Kantorovich generalized sampling series and a corresponding quantitative version in terms of the rst order of modulus of continuity. Further, we study the order of approximation in C(R), the set of all uniformly continuous and bounded functions on R for the family (Kφ wf)w>0. Finally, we give some examples of kernels such as B-spline kernels and the Blackman-Harris kernel to which the theory can be applied.

참고문헌 (29)

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