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Approximation by Stancu-Chlodowsky type lambda-Bernstein operators

Mursaleen M., Al-Abied A. A. H., Salman M. A.

Journal of Applied Analysis

2020

Vol. 26, nr 1

97--110

In this paper,we give some approximation properties by Stancu-Chlodowsky type λ-Bernstein operators in the polynomial weighted space and obtain the convergence properties of these operators by using Korovkin’s theorem. We also establish the direct result and the Voronovskaja type asymptotic formula.

Certain generalized q-operators

Prakash O., Sharma D., Maheshwari P.

Demonstratio Mathematica

2015

Vol. 48, nr 3

404--412

The applications of q-calculus in the approximation theory is a very interesting area of research in the recent years, several new q-operators were introduced and their behaviour were discussed by many researchers. This paper is the extension of the paper [15], in which Durrmeyer type generalization of q-Baskakov–Stancu type operators were discussed by using the concept of q-integral operators. Here, we propose to study the Stancu variant of q-Baskakov–Stancu type operators. We establish an estimate for the rate of convergence in terms of modulus of continuity and weighted approximation properties of these operators.