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On the Durrmeyer type modification of the \(q\)-Baskakov type operators. (English) Zbl 1180.41012

Summary: This paper deals with Durrmeyer type generalization of \(q\)-Baskakov type operators using the concept of \(q\)-integral, which introduces a new sequence of positive \(q\)-integral operators. We show that this sequence is an approximation process in the polynomial weighted space of continuous functions defined on the interval \([0,\infty)\). An estimate for the rate of convergence and weighted approximation properties are also obtained.

MSC:

41A25 Rate of convergence, degree of approximation
41A36 Approximation by positive operators
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