Weighted Approximation by New Bernstein-Chlodowsky-Gadjiev Operators

Abstract

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 -> infinity 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 b(n) 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.