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Open AccessArticle

Approximation Properties of an Extended Family of the Szász–Mirakjan Beta-Type Operators

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Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
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Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
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Department of Mathematics, Gazi University, Ankara TR-06500, Turkey
*
Author to whom correspondence should be addressed.
Axioms 2019, 8(4), 111; https://doi.org/10.3390/axioms8040111
Received: 14 September 2019 / Revised: 28 September 2019 / Accepted: 30 September 2019 / Published: 10 October 2019
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
Approximation and some other basic properties of various linear and nonlinear operators are potentially useful in many different areas of researches in the mathematical, physical, and engineering sciences. Motivated essentially by this aspect of approximation theory, our present study systematically investigates the approximation and other associated properties of a class of the Szász-Mirakjan-type operators, which are introduced here by using an extension of the familiar Beta function. We propose to establish moments of these extended Szász-Mirakjan Beta-type operators and estimate various convergence results with the help of the second modulus of smoothness and the classical modulus of continuity. We also investigate convergence via functions which belong to the Lipschitz class. Finally, we prove a Voronovskaja-type approximation theorem for the extended Szász-Mirakjan Beta-type operators. View Full-Text
Keywords: gamma and beta functions; Szász-Mirakjan operators; Szász-Mirakjan Beta type operators; extended Gamma and Beta functions; confluent hypergeometric function; Modulus of smoothness; modulus of continuity; Lipschitz class; local approximation; Voronovskaja type approximation theorem gamma and beta functions; Szász-Mirakjan operators; Szász-Mirakjan Beta type operators; extended Gamma and Beta functions; confluent hypergeometric function; Modulus of smoothness; modulus of continuity; Lipschitz class; local approximation; Voronovskaja type approximation theorem
MDPI and ACS Style

Srivastava, H.M.; İçöz, G.; Çekim, B. Approximation Properties of an Extended Family of the Szász–Mirakjan Beta-Type Operators. Axioms 2019, 8, 111.

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