A new class of gamma-type operator and its improvement: theory and numerical experiments

Abstract

The convergence rate of existing positive linear operators for a given function f under certain conditions, is often very slow. So, the researchers have focused on developing techniques to increase the convergence rates of these positive linear operators. This paper introduces a novel class of positive linear operators of gamma-type of order one and then a new second-order improved version of the operator is also given. Detailed proofs for the uniform convergence, asymptotic order of convergence, and other essential properties are provided. Additionally, two discrete forms of these operators, designed for numerical applications, are introduced. Finally, several examples are included at the end to validate the theoretical results. © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2025.