A New Sequence of Bernstein-Durrmeyer Operators and Their $L_p$-Approximation Behaviour

Year 2023, Volume: 11 Issue: 4, 198 - 212, 25.10.2023

Harun Çiçek Aydın İzgi Nadeem Rao

Abstract

The purpose of the present manuscript is to present a new sequence of Bernstein-Durrmeyer operators. First, we investigate approximation behaviour for these sequences of operators in Lebesgue Measurable space. Further, we discuss rate of convergence and order of approximation with the aid of Korovkin theorem, modulus of continuity and Peetre K-functional in $l_p$ space. Moreover, Voronovskaja type theorem is introduced to approximate a class of functions which has first and second order continuous derivatives. In the last section, numerical and graphical analysis are investigated to show better approximation behaviour for these sequences of operators.

Keywords

Rate of convergence, order of approximation;, modulus of continuity;, Bernstein-Durrmeyer operators.

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