Approximation by α‐Chlodowsky–Durrmeyer Operators

ABSTRACT The main objective of this article is to construct a new sequence of ‐Chlodowsky–Durrmeyer type operators including shape parameter , where . We compute some needed moment estimates. Also, we study some direct and local approximation properties of the proposed operators. Next, we obtain the order of convergence in terms of the weighted modulus of continuity. Then, in order to check the asymptotic behavior of related operators, we prove Voronovskaya's type theorem. Further, we evaluate pointwise convergence of the proposed operators. To validate our theoretical results, we perform some graphical and numerical experiments that illustrate the precision, effectiveness, and advantages of the proposed approach in practical applications of the related operators.