Approximation of some Feller semigroups associated with a modification of Szász–Mirakjan–Kantorovich operators

Montano, Mirella Cappelletti; Leonessa, Vita

doi:10.1007/s10474-012-0267-7

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“…introduced and studied the generalized Szász-Mirakjan-Kantorovich operators in [5]. Also in [15], the authors obtained some qualitative properties and an asymptotic formula for such a sequence of operators.…”

Section: Introductionmentioning

confidence: 99%

Approximation by generalized Kantorovich sampling type series

Kumar¹,

Devaraj²

2017

Preprint

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In the present article, we analyse the behaviour of a new family of Kantorovich type sampling operators (K ϕ w f ) w>0 . First, we give a Voronovskaya type theorem for these Kantorovich generalized sampling series and a corresponding quantitative version in terms of the first 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 (K ϕ w f ) w>0 . Finally, we give some examples of kernels such as B-spline kernels and Blackman-Harris kernel to which the theory can be applied.

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Section: Introductionmentioning

confidence: 99%