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Jakimovski–Leviatan operators of Kantorovich type involving multiple Appell polynomials

Pooja Gupta, Ana Maria Acu and Purshottam Narain Agrawal

Abstract

The purpose of the present paper is to obtain the degree of approximation in terms of a Lipschitz type maximal function for the Kantorovich type modification of Jakimovski–Leviatan operators based on multiple Appell polynomials. Also, we study the rate of approximation of these operators in a weighted space of polynomial growth and for functions having a derivative of bounded variation. A Voronvskaja type theorem is obtained. Further, we illustrate the convergence of these operators for certain functions through tables and figures using the Maple algorithm and, by a numerical example, we show that our Kantorovich type operator involving multiple Appell polynomials yields a better rate of convergence than the Durrmeyer type Jakimovski Leviatan operators based on Appell polynomials introduced by Karaisa (2016).

MSC 2010: 26A15; 41A35; 26A45

Funding statement: The first author is thankful to the “Ministry of Human Resource and Development”, New Delhi, India, and the second author is thankful to Lucian Blaga University of Sibiu Project research grants LBUS-IRG-2017-03 for the financial support to carry out the above research.

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Received: 2017-02-22
Revised: 2017-07-27
Accepted: 2017-08-09
Published Online: 2019-03-08
Published in Print: 2021-02-01

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