Quantitative Theorems for a Rich Class of Novel Miheşan-type Approximation Operators Incorporating the Boas-Buck Polynomials

Dhruv Bhatnagar
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Dhruv Bhatnagar: Delft University of Technology (TU Delft)

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 4, 1017-1035

Abstract: Abstract In this work, new summation-integral approximation operators based on a versatile generalization of the classic Szász-Mirakjan type operators, and incorporating the Boas-Buck polynomials are considered. We show how the proposed operators can get reduced to a multitude of operators involving classic approximation operators studied over past many decades. Wex nomenclate the individual cases hybrid generalizations of Bernstein, Baskakov, Lupaş and Szász-Mirakjan operators, each incorporating the Boas-Buck, Brenke, Sheffer and Appell polynomials. Indispensable properties of the proposed operators based on first and second order modulus of continuity are derived. Approximation on weighted space is also considered. In addition, quantitative Voronovskaja-type theorems have very recently been acknowledged as valuable properties for approximating functions. These form a noteworthy part of the present work.

Keywords: Weighted modulus of continuity; Boas-Buck polynomials; Steklov mean (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00216-3

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