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

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.

A new weighted statistical convergence and some associated approximation theorems

“…For more results related to this Theorem, see previous works. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] Denote the space of all continuous functions on I = [0, ∞) by C(I).…”

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“…This section deals with estimates of the differences between classical operators and modified operators. Very recently, estimates of the differences of certain positive linear operators were obtained in [14][15][16][17][18].…”

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