An Efficient Iterative Scheme for Approximating the Fixed Point of a Function Endowed with Condition (Bγ,μ) Applied for Solving Infectious Disease Models

The purpose of this paper is to construct a new fixed-point iterative scheme, called the Picard-like iterative scheme, for approximating the fixed point of a mapping that satisfies condition (Bγ,μ) in the setting of a uniformly convex Banach space. We prove that this novel iterative scheme converges faster than some existing iterative schemes in the literature. Moreover, G-stability and almost G-stability results are proven. Furthermore, we apply our results for approximating the solution of an integral equation that models the spread of some infectious diseases. Similarly, we also applied the results for approximating the solution of the boundary value problem by embedding Green’s function in our novel method. Our results extend and generalize other existing results in the literature.