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

Harun Çiçek; Aydın İzgi; Nadeem Rao

doi:10.36753/mathenot.1160715

EN

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

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.

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Harun Çiçek ^*
0000-0003-3018-3015
Türkiye

Aydın İzgi
0000-0003-3715-8621
Türkiye

Nadeem Rao
0000-0002-5681-9563
Türkiye

Early Pub Date

August 8, 2023

Publication Date

October 25, 2023

Submission Date

August 11, 2022

Acceptance Date

November 10, 2022

Published in Issue

Year 2023 Volume: 11 Number: 4

DOI

https://doi.org/10.36753/mathenot.1160715

IZ

https://izlik.org/JA66KF95CF

APA

Çiçek, H., İzgi, A., & Rao, N. (2023). A New Sequence of Bernstein-Durrmeyer Operators and Their $L_p$-Approximation Behaviour. Mathematical Sciences and Applications E-Notes, 11(4), 198-212. https://doi.org/10.36753/mathenot.1160715

AMA

1.Çiçek H, İzgi A, Rao N. A New Sequence of Bernstein-Durrmeyer Operators and Their $L_p$-Approximation Behaviour. Math. Sci. Appl. E-Notes. 2023;11(4):198-212. doi:10.36753/mathenot.1160715

Chicago

Çiçek, Harun, Aydın İzgi, and Nadeem Rao. 2023. “A New Sequence of Bernstein-Durrmeyer Operators and Their $L_p$-Approximation Behaviour”. Mathematical Sciences and Applications E-Notes 11 (4): 198-212. https://doi.org/10.36753/mathenot.1160715.

EndNote

Çiçek H, İzgi A, Rao N (October 1, 2023) A New Sequence of Bernstein-Durrmeyer Operators and Their $L_p$-Approximation Behaviour. Mathematical Sciences and Applications E-Notes 11 4 198–212.

IEEE

[1]H. Çiçek, A. İzgi, and N. Rao, “A New Sequence of Bernstein-Durrmeyer Operators and Their $L_p$-Approximation Behaviour”, Math. Sci. Appl. E-Notes, vol. 11, no. 4, pp. 198–212, Oct. 2023, doi: 10.36753/mathenot.1160715.

ISNAD

Çiçek, Harun - İzgi, Aydın - Rao, Nadeem. “A New Sequence of Bernstein-Durrmeyer Operators and Their $L_p$-Approximation Behaviour”. Mathematical Sciences and Applications E-Notes 11/4 (October 1, 2023): 198-212. https://doi.org/10.36753/mathenot.1160715.

JAMA

1.Çiçek H, İzgi A, Rao N. A New Sequence of Bernstein-Durrmeyer Operators and Their $L_p$-Approximation Behaviour. Math. Sci. Appl. E-Notes. 2023;11:198–212.

MLA

Çiçek, Harun, et al. “A New Sequence of Bernstein-Durrmeyer Operators and Their $L_p$-Approximation Behaviour”. Mathematical Sciences and Applications E-Notes, vol. 11, no. 4, Oct. 2023, pp. 198-12, doi:10.36753/mathenot.1160715.

Vancouver

1.Harun Çiçek, Aydın İzgi, Nadeem Rao. A New Sequence of Bernstein-Durrmeyer Operators and Their $L_p$-Approximation Behaviour. Math. Sci. Appl. E-Notes. 2023 Oct. 1;11(4):198-212. doi:10.36753/mathenot.1160715