Approximation by sampling Kantorovich series in weighted spaces of functions

Authors: TUNCER ACAR, OSMAN ALAGÖZ, ALİ ARAL, DANİLO COSTARELLİ, METİN TURGAY, GIANLUCA VINTI

Abstract: This paper studies the convergence of the so-called sampling Kantorovich operators for functions belonging to weighted spaces of continuous functions. This setting allows us to establish uniform convergence results for functions that are not necessarily uniformly continuous and bounded on $\mathbb{R}$. In that context we also prove quantitative estimates for the rate of convergence of the family of the above operators in terms of weighted modulus of continuity. Finally, pointwise convergence results in quantitative form by means of Voronovskaja type theorems have been also established.

Keywords: Generalized sampling series, sampling Kantorovich operators, pointwise and uniform convergence, weighted approximation, asymptotic formulas

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