Approximation by half Bernstein polynomials

Muslim, Hadeel O.; Mohammad, Ali J.

doi:10.47974/JIM-1884

Open Access Research Article

Approximation by half Bernstein polynomials

^*Hadeel O. MuslimCorresponding authorhadeel.o.alkhaled@uodiyala.edu.iqDepartment of Mathematics College of Science Diyala UniversityDepartment of Mathematics Diyala University Diyala, IraqView full profile → , Ali J. Mohammadibtihaljas.moh@gmail.comDepartment of Mathematics College of Science Diyala UniversityDepartment of Mathematics University of BasrahBasrah, IraqView full profile →

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pp. 865–869Vol. 27Issue 4June 2024DOI: 10.47974/JIM-1884XML

Received:: 10 Jan 2024
Published Online:: 30 Jun 2024
Article type:: Research Article
Language:: EN
Article no.:: JIM-1884
Pages:: 865–869

Abstract

This paper defines and studies the half Bernstein polynomials to approximate functions in C[0,1]. The pointwise convergence in ordinary approximation is given for these polynomials. Also, the order of approximation, the Voronovskaya-type asymptotic theorem and the error estimate are introduced. Finally, to show the ability convergence of these polynomials we provide some examples to approximate these polynomials to test functions and compare numerical results with the results corresponding to classical Bernstein polynomials.

Keywords

Linear positive operators Ordinary approximation Order of approximation Modulus of continuity Bernstein sequence

Subject Classifications

41A1041A2541A36

References

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