Convergence analysis of an accelerated iteration for monotone generalized \(\alpha\)-nonexpansive mappings with a partial order (Q2422472)

Summary: In this paper, we introduce a new accelerated iteration for finding a fixed point of monotone generalized \(\alpha\)-nonexpansive mapping in an ordered Banach space. We establish some weak and strong convergence theorems of fixed point for monotone generalized \(\alpha\)-nonexpansive mapping in a uniformly convex Banach space with a partial order. Further, we provide a numerical example to illustrate the convergence behavior and effectiveness of the proposed iteration process.