# Approximation by Generalized Kantorovich Sampling Type Series

• Kumar, Angamuthu Sathish (Department of Mathematics, Visvesvaraya National Institute of Technology) ;
• Devaraj, Ponnaian (Department of Mathematics, Indian Institute of Science Education and Research)
• Accepted : 2019.01.28
• Published : 2019.09.23
• 14 2

#### Abstract

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

#### Keywords

sampling Kantorovich operators;Voronovskaya type formula;rate of convergence;modulus of smoothness

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