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Weighted approximation by new Bernstein-Chlodowsky-Gadjiev operators

Aral Ali (Kirikkale University, Faculty of Science and Arts, Department of Mathematics, Yahşihan, Kirikkale, Turkey)
Acar Tuncer (Kirikkale University, Faculty of Science and Arts, Department of Mathematics, Yahşihan, Kirikkale, Turkey)

In the present paper, we introduce Bernstein-Chlodowsky-Gadjiev operators taking into consideration the polynomials introduced by Gadjiev and Ghorbanalizadeh [2]. The interval of convergence of the operators is a moved interval as polynomials given in [2] but grows as n ( ∞ as in the classical Bernstein-Chlodowsky polynomials. Also their knots are shifted and depend on x. We firstly study weighted approximation properties of these operators and show that these operators are more efficient in weighted approximating to function having polynomial growth since these operators contain a factor bn tending to infinity. Secondly we calculate derivative of new Bernstein-Chlodowsky-Gadjiev operators and give a weighted approximation theorem in Lipchitz space for the derivatives of these operators.

Keywords: Bernstein-Chlodowsky-Gadjiev operators, weighted approximation, Lipschitz space