Approximation by a new Stancu variant of generalized (λ,μ)-Bernstein operators

Abstract

The primary objective of this work is to explore various approximation properties of Stancu variant generalized (λ,μ)-Bernstein operators. Various moment estimates are analyzed, and several aspects of local direct approximation theorems are investigated. Additionally, further approximation features of newly defined operators are delved into, such as the Voronovskaya-type asymptotic theorem and pointwise estimates. By comparing the proposed operator graphically and numerically with some linear positive operators known in the literature, it is evident that much better approximation results are achieved in terms of convergence behavior, calculation efficiency, and consistency. Finally, the newly defined operators are used to obtain a numerical solution for a special case of the fractional Volterra integral equation of the second kind.

Keywords

• λ-Bernstein operators
• Computer graphics
• Fractional integral equations
• Error analysis
• Pointwise estimates