A Parametric Generalization of the Baskakov-Schurer-Szász-Stancu Approximation Operators

Symmetry

NaimLatif Braha¹  HariMohan Srivastava²  Toufik Mansour³ 

[1] Department of Mathematics and Computer Sciences, University of Prishtina, Avenue “Mother Tereza” Nr. 5, 10000 Prishtinë, Kosova;Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada;Department of Mathematics, University of Haifa, Haifa 3498838, Israel;

关键词: approximation operators;    parametric generalization;    Baskakov-Schurer-Szász-Stancu operators;    Korovkin type theorem;    Voronovskaya type theorem;    rate of convergence;   

DOI  :  10.3390/sym13060980

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown