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Solving Fractional Volterra-Fredholm Integro-Differential Equations via A** Iteration Method

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In this article, we develop a faster iteration method, called the A** iteration method, for approximating the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. We establish some… Click to show full abstract

In this article, we develop a faster iteration method, called the A** iteration method, for approximating the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. We establish some weak and strong convergence results of the A** iteration method for fixed points of generalized α-nonexpansive mappings in uniformly convex Banach spaces. We provide a numerical example to illustrate the efficiency of our new iteration method. The weak w2-stability result of the new iteration method is also studied. As an application of our main results, we approximate the solution of a fractional Volterra–Fredholm integro-differential equation. Our results improve and generalize several well-known results in the current literature.

Keywords: fredholm integro; fractional volterra; iteration method; volterra fredholm; iteration

Journal Title: Axioms
Year Published: 2022

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