A Parametric Generalization of the Baskakov-Schurer-Szász-Stancu Approximation Operators
Date
2021
Authors
Latif Braha, Naim
Mansour, Toufik
Srivastava, H.M.
Journal Title
Journal ISSN
Volume Title
Publisher
Symmetry
Abstract
In this paper, we introduce and investigate a new class of the parametric generalization of
the Baskakov-Schurer-Szász-Stancu operators, which considerably extends the well-known class of
the classical Baskakov-Schurer-Szász-Stancu approximation operators. For this new class of approximation
operators, we present a Korovkin type theorem and a Grüss-Voronovskaya type theorem, and
also study the rate of its convergence. Moreover, we derive several results which are related to the
parametric generalization of the Baskakov-Schurer-Szász-Stancu operators in the weighted spaces.
Finally, we prove some shape-preserving properties for the parametric generalization of the Baskakov-
Schurer-Szász-Stancu operators and, as a special case, we deduce the corresponding shape-preserving
properties for the classical Baskakov-Schurer-Szász-Stancu approximation operators.
Description
Keywords
approximation operators, parametric generalization, Baskakov-Schurer-Szász-Stancu operators, Krovkin type theorem, Voronovskaya type theorem, rate of convergence, Grüss-Voronovskaya type theorem, shape-preserving properties
Citation
Latif Braha, N., Mansour, T., & Srivastava, H. M. (2021). A Parametric Generalization of the Baskakov-Schurer-Szász-Stancu Approximation Operators. Symmetry, 13(6), 1-24. https://doi.org/10.3390/sym13060980.