Advances in Operator Theory

Approximation by Chlodowsky variant of Szász operators involving Sheffer polynomials

Khursheed J‎. ‎Ansari, M. ‎Mursaleen, and A. H. ‎Al-Abeid

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‎‎‎In this article‎, ‎we present a Chlodowsky type variation of Szász operators defined by means of the Sheffer type polynomials‎. ‎We established convergence properties and the order of‎ ‎convergence through a classical approach‎, ‎the second order modulus of continuity‎, ‎Peetre's $K$-functional‎, ‎and a new type of weighted modulus of continuity‎. ‎Furthermore‎, ‎$A$-statistical approximation of Korokin type for the operators is also shown and the rate of convergence of operators for functions having derivatives of bounded variation is also obtained‎. ‎Moreover‎, ‎some numerical and graphical examples are also given to support our results‎.

Article information

Adv. Oper. Theory, Volume 4, Number 2 (2019), 321-341.

Received: 23 April 2018
Accepted: 30 June 2018
First available in Project Euclid: 27 July 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 41A10: Approximation by polynomials {For approximation by trigonometric polynomials, see 42A10}
Secondary: 41A25‎ ‎41A28‎ ‎41A36

Szász operator‎ ‎ ‎rate of convergence weighted approximation ‎$A$-statistical approximation function of bounded variation


‎Ansari, Khursheed J‎.; ‎Mursaleen, M.; ‎Al-Abeid, A. H. Approximation by Chlodowsky variant of Szász operators involving Sheffer polynomials. Adv. Oper. Theory 4 (2019), no. 2, 321--341. doi:10.15352/aot.1804-1350.

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