Approximation of functions by a new class of generalized Bernstein–Schurer operators

In this work, we construct a new kind of Bernstein–Schurer operators which includes non-negative real parameter α . We study some shape preserving properties, namely, monotonicity and convexity of the new operators. We obtain global approximation formula in terms of Ditzian–Totik uniform modulus of...

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Bibliographic Details
Published inRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 114; no. 4
Main Authors Özger, Faruk, Srivastava, H. M., Mohiuddine, S. A.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2020
Springer Nature B.V
Subjects
Applications of Mathematics
Approximation
Convexity
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operators (mathematics)
Original Paper
Smoothness
Theoretical
Bernstein operators
Uniform convergence
41A35
41A36
Bernstein–Schurer
Shape preserving property
41A10
Global approximation
Voronovskaja-type approximation theorem
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Summary:In this work, we construct a new kind of Bernstein–Schurer operators which includes non-negative real parameter α . We study some shape preserving properties, namely, monotonicity and convexity of the new operators. We obtain global approximation formula in terms of Ditzian–Totik uniform modulus of smoothness of first and second order and calculate the local direct estimate of the rate of convergence with the help of Lipschitz-type function for our operators. The Voronovskaja-type approximation theorems of the new operators are presented. Finally, in the last section, we provide some graphs, MATLAB code and numerical examples in order to illustrate the significance of our newly constructed operators.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-020-00903-6