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

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  • Dhruv Bhatnagar

    (Delft University of Technology (TU Delft))

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.

Suggested Citation

  • Dhruv Bhatnagar, 2022. "Quantitative Theorems for a Rich Class of Novel Miheşan-type Approximation Operators Incorporating the Boas-Buck Polynomials," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(4), pages 1017-1035, December.
    • Handle: RePEc:spr:indpam:v:53:y:2022:i:4:d:10.1007_s13226-021-00216-3
    DOI: 10.1007/s13226-021-00216-3
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    References listed on IDEAS

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    1. Sucu, Sezgin & Varma, Serhan, 2015. "Generalization of Jakimovski−Leviatan type Szasz operators," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 977-983.
    2. Acar, Tuncer, 2015. "Asymptotic Formulas for Generalized Szász–Mirakyan Operators," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 233-239.
    3. Sezgin Sucu & Serhan Varma, 2019. "Approximation by Sequence of Operators Involving Analytic Functions," Mathematics, MDPI, vol. 7(2), pages 1-10, February.
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