Abstract
We introduce positive linear operators which are combined with the Chlodowsky and Szász type operators and study some approximation properties of these operators in the space of continuous functions of two variables on a compact set. The convergence rate of these operators are obtained by means of the modulus of continuity. And we also obtain weighted approximation properties for these positive linear operators in a weighted space of functions of two variables and find the convergence rate for these operators by using the weighted modulus of continuity.
Highlights
Introduction and PreliminariesLet x ∈ R+0 = [0, ∞) and f ∈ C(R+0 )
We introduce positive linear operators which are combined with the Chlodowsky and Szasz type operators and study some approximation properties of these operators in the space of continuous functions of two variables on a compact set
We investigate the convergence of the sequence of linear positive operators Ln,m, defined on a weighted space of functions of two variables, and find the rate of this convergence by means of weighted modulus of continuity
Summary
Received 21 September 2013; Revised 15 April 2014; Accepted 23 April 2014; Published 13 May 2014. We introduce positive linear operators which are combined with the Chlodowsky and Szasz type operators and study some approximation properties of these operators in the space of continuous functions of two variables on a compact set. The convergence rate of these operators are obtained by means of the modulus of continuity. We obtain weighted approximation properties for these positive linear operators in a weighted space of functions of two variables and find the convergence rate for these operators by using the weighted modulus of continuity
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