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.
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference24 articles.
1. Generalization of Bernstein's polynomials to the infinite interval
2. Approximation des fonctions continues au moyen de polynômes de la forme e−nx∑k=0mnck,nxk;Mirakjan;C. R. (Doklady) Acad. Sci. URSS (New Ser.),1941
3. Szász–Mirakjan type operators providing a better error estimation
4. Approximation with an arbitrary order by generalized Szász-Mirakjan operators;Gal;Stud. Univ. Babeş-Bolyai Math.,2014
5. Approximation properties of the q-Szász-Mirakjan-Beta operators;Gupta;Indian J. Ind. Appl. Math.,2012
Cited by
29 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献