Approximation of functions of two variables by certain linear positive operators

Abstract

Abstract. We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using modulus of continuity. Moreover we define an rth order generalization of these operators and observe its approximation properties. Furthermore, we study the convergence of the linear positive operators in a weighted space of functions of two variables and find the rate of this convergence using weighted modulus of continuity.

On Approximation Properties of Two Variables of Modified Kantorovich-Type Operators

“…In many papers various modi…cations of operators K n (f ) were introduced and many authors studied their approximation properties in di¤erent function spaces (see [4,5,9,12,13,14,15,18]). In papers [1,2,8,11,14,15,16,17,21] were studied for f 2 C p where C p with …xed p 2 N 0 := f0; 1; 2; :::g denotes the polynomial weighted space generated by the weight function !…”

“…In many papers various modi…cations of operators K n (f ) were introduced and many authors studied their approximation properties in di¤erent function spaces (see [4,5,9,12,13,14,15,18]).…”

Approximation by Certain Linear Positive Operators of Two Variables

“…If we take ( , ) := ( ) and ( , ) := ℎ( ) in (5), then the operators , reduce to the Chlodowsky and Szász type operators, respectively. Approximation of functions of one or two variables by some positive linear operators in weighted spaces may be found in [1,2,[5][6][7][8].…”

On Convergence Properties of Szasz-Mirakyan-Bernstein Operators of two Variables

“…Some positive linear operators for the functions of two variables are introduced and investigated their approximation properties by the authors in [13,5,11,15,14,12,10,4].…”