The Combination of Bernstein Polynomials with Positive Functions Based on a Positive Parameter s

Authors

DOI:

https://doi.org/10.26713/cma.v13i3.1619

Keywords:

Bernstein polynomials, Modulus of smoothness, Quantitative Voronovskaja, Grüss-Voronovskaja

Abstract

This paper deals with a sequence of the combination of Bernstein polynomials with a positive function τ and based on a parameter s>−12. These polynomials have preserved the functions 1 and τ. First, the convergence theorem for this sequence is studied for a function f∈C[0,1]. Next, the rate of convergence theorem for these polynomials is descript by using the first, second modulus of continuous and Ditzian-Totik modulus of smoothness. Also, the Quantitative Voronovskaja and Gruss-Voronovskaja are obtained. Finally, two numerical examples are given for these polynomials by chosen a test function f∈C[0,1] and two functions for τ to show that the effect of the different values of s and the different chosen functions τ.

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References

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Published

25-12-2022
CITATION

How to Cite

Mohammad, A. J., & Kathem, R. F. (2022). The Combination of Bernstein Polynomials with Positive Functions Based on a Positive Parameter s. Communications in Mathematics and Applications, 13(3), 1237–1247. https://doi.org/10.26713/cma.v13i3.1619

Issue

Vol. 13 No. 3 (2022)

Section

Research Article

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