Approximation by generalized MKZ-operators in polynomial weighted spaces

Abstract

We prove some approximation properties of generalized Meyer-König and Zeller operators for differentiable functions in polynomial weighted spaces. The results extend some results proved in [1][2][3][7][8][9][10][11][12][13][14][15][16].

A class of linear positive operators in weighted spaces

“…When q = 1 all of the results of this paper is valid for the operators M n f, b n ; x defined by Rempulska and Skorupka [20]. …”

On Chlodowsky Variant of Baskakov Type Operators

“…Recently, linear positive operators and their Chlodowsky type generalizations have been widely studied by several authors [1,[3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], because this generalization allows us to investigate approximation properties of functions defined on the infinite interval [0,∞) by using the similar techniques and methods on the classical operators. The aim of this paper is to study some convergence properties of the operators L n ( f ;β n ,x) defined by (1.4) and modify the operators for differentiable functions, in order to improve the rate of convergence on the interval [0,β n ] extending infinity as n → ∞.…”

Some preservation properties of MKZ-Stancu type operators

“…In 2007, Rempulska and Skorupka [12] defined a generalization of MKZ operators on an unbounded interval as follows:…”

“…In this work, we construct Stancu type modification of the generalization of Meyer-König and Zeller operators (MKZ) defined in [12]. We show that the Lipschitz constant of a Lipschitz continuous function and the properties of the function of modulus of continuity can be retained by these operators.…”