Approximation Properties of an Extended Family of the Szász–Mirakjan Beta-Type Operators
Date
2019
Authors
Srivastava, H.M.
Içöz, Gürhan
Çekim, Bayram
Journal Title
Journal ISSN
Volume Title
Publisher
Axioms
Abstract
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.
Description
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
Citation
Srivastava, H.M., Içöz, G. & Çekim, B. (2019). Approximation Properties of an Extended Family of the Szász–Mirakjan Beta-Type Operators. Axioms, 8(4), 111. https://doi.org/10.3390/axioms8040111