Abstract
This paper deals with new type q-Baskakov-Beta-Stancu operators defined in the paper. First, we have used the properties of q-integral to establish the moments of these operators. We also obtain some approximation properties and asymptotic formulae for these operators. In the end we have also presented better error estimations for the q-operators.
Highlights
In the recent years, the quantum calculus (q-calculus) has attracted a great deal of interest because of its potential applications in mathematics, mechanics, and physics
Due to the applications of q-calculus in the area of approximation theory, q-generalization of some positive operators has attracted much interest, and a great number of interesting results related to these operators have been obtained
Several authors have proposed the q-analogues of different linear positive operators and studied their approximation behaviors
Summary
The quantum calculus (q-calculus) has attracted a great deal of interest because of its potential applications in mathematics, mechanics, and physics. Due to the applications of q-calculus in the area of approximation theory, q-generalization of some positive operators has attracted much interest, and a great number of interesting results related to these operators have been obtained (see, for instance, [1,2,3]). In this direction, several authors have proposed the q-analogues of different linear positive operators and studied their approximation behaviors.
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