New generalization of the power summability methods for Dunkl generalization of Szász operators via \(q\)-calculus. (English) Zbl 07909232
Mohiuddine, S. A. (ed.) et al., Approximation theory, sequence spaces and applications. Cham: Springer. Ind. Appl. Math., 83-117 (2022).
Summary: In this work we prove some properties of Dunkl generalization of Szász operators via \(q\)-calculus, by considering the new generalization of the power summability methods, such as uniform convergence of this type of operators, Korovkin type theorem. Then we have proved some results in the weighted spaces of continuous functions, Voronovskaya type theorem, Grüss-Voronovskaya type theorem. In the third section, we have proved some results related to the statistical convergence of the Dunkl generalization of Szász operators via \(q\)-calculus, by using the \(A\)-transformation. In the last section, we estimate the rates of pointwise approximation of Dunkl generalization of Szász operators via \(q\)-calculus for functions with derivatives of bounded variation.
For the entire collection see [Zbl 1521.41001].
For the entire collection see [Zbl 1521.41001].
MSC:
| 40A05 | Convergence and divergence of series and sequences |
| 41A36 | Approximation by positive operators |
Keywords:
Dunkl generalization of Szász operators via q-calculus; Korovkin type theorem; Voronovskaya type theorem; rate of convergence; Grüss-Voronovskaya; bounded variationReferences:
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