Convergence and Stability of a New Hybrid Iteration Scheme for a Contraction Operator in Banach Spaces with Applications

Annual Meeting in Mathematics 2024

Abstract

This paper aims to introduce a new hybrid iterative process and establish the strong convergence theorem and T-stability of the new hybrid iterative scheme via a contraction operator in Banach spaces. Further, we show that our iteration process is faster than several existing iteration processes. Our main result shows that the proposed iteration process converges faster than the Noor iteration in the sense of Berinde [V. Berinde, Iterative Approximation of Fixed points, Springer, Berlin, 2007]. We support our analytic proof by a numerical example in which we approximate the fixed point by a computer using MATLAB program. As an application, we apply the proposed method to generate polynomiographs.