Jain's operator: A new construction and applications in approximation theory

Abstract

The new and more comprehensive Jain‐type operators based on a function and two sequences of functions and have been introduced. This newly defined operator has an important place in which these three functions can create both existing and new operators with special selections. In order to show their approximation properties, we present direct approximation results and Voronovkskaya‐type results for these operators. Finally, we provide a series of numerical examples to show their performance visually.