The family of $ \lambda $-Bernstein-Durrmeyer operators based on certain parameters

Abstract

The primary goal of this paper is to present the generalization of \begin{document}$ \lambda $\end{document}-Bernstein operators with the assistance of a sequence of operators proposed by Mache and Zhou [24]. For these operators, I establish some approximation results using second-order modulus of continuity, Lipschitz space, Ditzian-Totik modulus of smoothness, and Voronovskaya type asymptotic results. I also indicate some graphical comparisons of my operators among existing operators for better presentation and justification using Matlab.