Linking of Bernstein-Chlodowsky and Szász-Appell-Kantorovich type operators

Volume 10, Issue 6, pp 3288--3302 http://dx.doi.org/10.22436/jnsa.010.06.39

Publication Date: June 25, 2017 Submission Date: April 18, 2017

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Authors

P. N. Agrawal - Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India. D. Kumar - Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India. S. Araci - Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, TR-27410, Gaziantep, Turkey.

Abstract

In the present paper, we define a sequence of bivariate operators by linking the Bernstein-Chlodowsky operators and the Szász-Kantorovich operators based on Appell polynomials. First, we establish the moments of the operators and then determine the rate of convergence of these operators in terms of the total and partial modulus of continuity. Next, we obtain the order of approximation of the considered operators in a weighted space. Furthermore, we define the associated GBS (Generalized Boolean Sum) operators of the linking operators and then study the rate of convergence with the aid of the Lipschitz class of Bögel continuous functions and the mixed modulus of smoothness.

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Keywords

• Appell polynomials
• weighted approximation
• GBS operators
• partial and mixed modulus of smoothness
• Peetre’s K-functional.

MSC

•  41A25
•  41A36
•  41A63
•  41A10

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