Abstract
We introduce a new sequence ofq-integral operators. We show that it is a weighted approximation process in the polynomial space of continuous functions defined on unit interval. Weighted statistical approximation theorem, Korovkin type theorems for fuzzy continuous functions, and an estimate for the rate of convergence for these operators.
Highlights
The study of q-Calculus is a generalization of any subjects, such as hyper geometric series, complex analysis, and particle physics
In this paper motivated by Sharma [6, 7, 10,11,12] we introduce a q-analogue of the q-Baskakov-Durrmeyer type operators defined as follows: for f ∈ CIn,q, (Mn,qf) (x)
In this paper, motivated by Kasana and Sharma, we introduce a q-analogue of the q-Baskakov-Durrmeyer type operators defined as follows: for f ∈ CIn,q, (Mn⋆,q,xf) (t)
Summary
The study of q-Calculus is a generalization of any subjects, such as hyper geometric series, complex analysis, and particle physics. In this paper motivated by Sharma we introduced a q-analogue of the q-Durrmeyer operators and we study better rate of convergence and statistical approximation properties. Sharma [6] introduced the following q-Durrmeyer type operators defined as follows: for f ∈ CIn,q, where In,q = [0, [n]q/[n + 1]q],. In this paper motivated by Sharma [6, 7, 10,11,12] we introduce a q-analogue of the q-Baskakov-Durrmeyer type operators defined as follows: for f ∈ CIn,q,. In this paper, motivated by Kasana and Sharma, we introduce a q-analogue of the q-Baskakov-Durrmeyer type operators defined as follows: for f ∈ CIn,q,. The aim of this paper is to study some approximation properties of a new generalization of operators based on qintegers. We give better error estimations for operators (10) and (12)
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