Fixed point approximation via a new faster iteration process in Banach spaces with an application

Abstract

In this paper, we propose a new iterative process for approximating fixed points of mappings. First, we prove that our iterative scheme is faster than the iterative processes of Thakur and Piri for contractive mapping in Banach spaces. To support the analytical results, we give some numerical examples using the software program MATLAB. Afterwards, we give some weak and strong convergence theorems for monotone generalized α-nonexpansive mapping in uniformly convex ordered Banach spaces. To justify the utility of our main results, we presented an application regarding the approximation of the solution to an integral equation, supported by an illustrative example.