Differences of Positive Linear Operators on Simplices

Abstract

The aim of the paper is twofold: we introduce new positive linear operators acting on continuous functions defined on a simplex and then estimate differences involving them and/or other known operators. The estimates are given in terms of moduli of smoothness and K -functionals. Several applications and examples illustrate the general results.

Approximation Properties of Linear Positive Operators with Differences

“…operators involved are usually on continuous functions defined on real intervals. Aral-Inoan-Rasa [9], Acu et al [10], V. Gupta [11], Gupta-Tachev [12] discovered some noteworthy results on difference of such operators.…”

Convergence Theorems for Derivatives of a New Baskakov -Type Operators

“…Some papers were recruit to find the derivatives of a sequence of positive and linear operators and to study them properties by some authors, it is possible to review the references ( [11]- [14]).…”

On difference of bivariate linear positive operators

“…In 2021, A. M. Acu et al gave some theorems for the difference of linear positive operators of two variables defined on a simplex [4].…”