Higher order Kantorovich-type Szász–Mirakjan operators

Abstract

In this paper, we define new higher order Kantorovich-type Szász–Mirakjan operators, we give some approximation properties of these operators in terms of various moduli of continuity. We prove a local approximation theorem, a Korovkin-type theorem, and a Voronovskaja-type theorem. We also prove weighted approximation theorems for these new operators.

Shape Preserving Properties of Parametric Szász Type Operators on Unbounded Intervals

“…From this point of view, studying the shape preserving properties of operators is a very important part of the function approximation theory. In order to be more effectively applied to CAGD on infinite intervals, some kinds of Sz ász operators based on nonnegative parameters were introduced [7][8][9][10][11][24][25][26]. In 1998, Carbone et al obtained the shape preserving properties of the Sz ász operators by probabilistic methods [16][17][18].…”

Shape Preserving Properties of Parametric Szasz Type Operators on Unbounded Intervals

“…From this point of view, studying the shape preserving properties of operators is a very important part of the function approximation theory. In order to be more effectively applied to CAGD on infinite intervals, some kinds of Sz ász operators based on nonnegative parameters were introduced [7][8][9][10][11][24][25][26]. In 1998, Carbone et al obtained the shape preserving properties of the Sz ász operators by probabilistic methods [16][17][18].…”