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Quantitative-Voronovskaja-type theorems for novel generalized-Szász–Durrmeyer operators incorporating the Sheffer sequences

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Abstract

In this work, a novel hybrid approximation operator based on a versatile generalization of the classic Szász–Mirakjan operators, and incorporating the Sheffer sequences is considered. It is demonstrated how the proposed operators can get reduced to a multitude of operators involving classic approximation operators studied over past many decades. We call the individual cases generalized Bernstein, Baskakov, Lupaş and Szász–Mirakjan operators, each incorporating the 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 studied. Further, quantitative Voronovskaja-type theorems have very recently been acknowledged as valuable approximation properties. These form a momentous part of the present work. We conclude with an explicit graphical demonstration of approximation by the proposed operators in the case of the Sheffer sequence reduced to the Bell polynomials.

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Authors and Affiliations

  1. Technische Universiteit Delft, Delft, The Netherlands

    Dhruv Bhatnagar

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Communicated by Samy Ponnusamy.

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Bhatnagar, D. Quantitative-Voronovskaja-type theorems for novel generalized-Szász–Durrmeyer operators incorporating the Sheffer sequences. J Anal 31, 475–499 (2023). https://doi.org/10.1007/s41478-022-00467-1

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