Fixed Point Approximation of Generalized α-Non-Expansive Multi-Valued Mapping in Convex Metric Space

In this paper, we present approximation results for a generalized α-non-expansive multi-valued mapping using a four-step iteration scheme introduced in the context of a convex metric space. We extend some recent results about generalized α-non-expansive multi-valued mappings from the Banach space setting to a convex metric space. Two examples of generalized α-non-expansive multi-valued mappings are presented, and it is numerically shown that our iteration scheme enables faster convergence than other well-known schemes in the literature. To demonstrate the application of one of our results, we provide the solution of a non-linear integral equation.