On Some Approximation Properties for a Sequence of λ-Bernstein Type Operators

Authors

  • Ali Jassim Muhammad
  • Asma Jaber

DOI:

https://doi.org/10.24996/ijs.2021.62.12.28

Keywords:

λ-Bernstein polynomials, Voronovaskaja type asymptotic formula, the uniform convergence, ordinary and simultaneous approximations

Abstract

In 2010, Long and Zeng introduced a new generalization of the Bernstein polynomials that depends on a parameter  and called -Bernstein polynomials. After that, in 2018, Lain and Zhou studied the uniform convergence for these -polynomials and obtained a Voronovaskaja-type asymptotic formula in ordinary approximation. This paper studies the convergence theorem and gives two Voronovaskaja-type asymptotic formulas of the sequence of -Bernstein polynomials in both ordinary and simultaneous approximations. For this purpose, we discuss the possibility of finding the recurrence relations of the -th order moment for these polynomials and evaluate the values of -Bernstein for the functions ,  is a non-negative integer

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Published

2021-12-30

How to Cite

Muhammad, A. J. ., & Jaber, A. . (2021). On Some Approximation Properties for a Sequence of λ-Bernstein Type Operators. Iraqi Journal of Science, 62(12), 4903–4915. https://doi.org/10.24996/ijs.2021.62.12.28

Issue

Section

Mathematics