On a Novel Class of (Λ, Ν)-Bernstein Operators: Approximation Results on Bogel Spaces and Associated Graphical Error Estimates

Abstract

In this paper, we consider a novel sequence of modified bivariate Bernstein-Stancu operators and investigate some precious approximation properties of proposed operators. With the aid of two-dimensional test functions and central moments, we derive essential estimates to establish uniform convergence and determine the order of approximation. Additionally, we present local approximation results in the context of Lipschitz maximal functions. Furthermore, we explore the applicability of these operators in Bogel spaces and employ the mixed modulus of continuity to evaluate their performance. To validate our theoretical results, we perform numerical experiments that illustrate the precision, effectiveness and advantages of the proposed approach in practical applications of the proposed operators.