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

Abstract

<p style='text-indent:20px;'>The primary goal of this paper is to present the generalization of <inline-formula><tex-math id="M2">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>-Bernstein operators with the assistance of a sequence of operators proposed by Mache and Zhou [<xref ref-type="bibr" rid="b24">24</xref>]. 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.</p>