Convergence Behavior of Modified-Bernstein-Kantrovinch-Stancu Operators

Modified-Bernstein-Kantrovinch-Stancu Operators

Abstract

The study introduces a Kantrovinch-Stancu type modification of the modified-Bernstein operator, examining its convergence properties for H\"{o}lder's class of functions. It evaluates the rate of convergence through the modulus of continuity and Peetre's K-functional, providing insights into the efficiency of the proposed operators. Additionally, the research establishes a Vornovskaya type asymptotic result and investigates weighted approximation with polynomial growth, shedding light on the behavior of approximations under varying conditions. To illustrate the convergence behavior empirically, the study employs MATLAB software to present numerical examples, offering tangible evidence of the theoretical findings. Through this comprehensive analysis, the study contributes to understanding the performance and applicability of the Kantrovinch-Stancu modification in approximation theory, with implications for various fields relying on function approximation techniques.