Convergence of Iterates of α-Bernstein Type Operators via Fixed Point of Generalized JS-Contraction Type Mappings

Abstract

The aim of this paper is to establish Kelisky-Rivlin type theorem for α-Bernstein-type operators. To achieve this, we first introduce the concept of a generalized JS-contraction type mapping and then we prove a fixed point theorem which is new and first of its kind in the known literature on fixed point theory. The result presented herein generalizes and improves the main result of Altun et al. [Altun, I., Al Arifi, N., Jleli, M., Lashin, A., Samet, B. (2017). A fixed point theorem for JS-contraction type mappings with applications to polynomial approximations. Filomat. 31(15):4969-4978].

Keywords:

• α-Bernstein operators
• Fixed point
• JS-contraction

Acknowledgements

The authors are grateful to the Editor-in-Chief and anonymous Referees for their valuable comments towards the improvement of the original version of the manuscript.