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 BaskakovSchurer-Szász-Stancu operators and, as a special case, we deduce the corresponding shape-preserving properties for the classical Baskakov-Schurer-Szász-Stancu approximation operators.
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- Approximation operators
- Baskakov-Schurer-Szász-Stancu operators
- Grüss-Voronovskaya type theorem
- Korovkin type theorem
- Parametric generalization
- Rate of convergence
- Shape-preserving properties
- Voronovskaya type theorem
ASJC Scopus subject areas
- Computer Science (miscellaneous)
- Chemistry (miscellaneous)
- General Mathematics
- Physics and Astronomy (miscellaneous)