An Algorithm for Nonlinear Problems Based on Fixed Point Methodologies With Applications

This research presents a highly efficient fixed point algorithm for the computation of fixed points for a very general class of nonexpansive mappings called generalized (α, β)-nonexpansive mappings within the context of uniformly convex Banach space. Our research establishes both weak and strong convergence theorems of the scheme. Furthermore, we demonstrate that the class of generalized (α, β)-nonexpansive mappings contain many classes of nonlinear mappings of the classical literature. Then, we perform various numerical computations to prove the efficiency of the proposed approach. We also study the convergence analysis of the scheme for two dimensional space with taxicab norm. Moreover, we show that our new result gives an alternative approach for solving Caputo fractional differential equation in a novel mappings setting.