A new class of positive linear operators and their improvement: theory and numerical experiments

Abstract

As far as we know, the main drawback of the classical positive linear operators of a given function f (under suitable conditions) is that they are of order one. Thus they converge to f very slowly. This paper presents a new class of integral-type positive linear operators that are of order one. Additionally, a second-order improvement of the operator is also provided. Uniform convergence, asymptotic order of convergence and other important properties are proved in detail. Two discrete forms of the operators suitable for numerical purposes are also introduced. Several examples are given in the end to verify the theoretical results numerically. © 2025 Informa UK Limited, trading as Taylor & Francis Group.