Alghamdi et al. Iteration Scheme for Hemicontractive Operators in Arbitrary Banach Spaces.

The purpose of this paper is to characterize the conditions for the convergence of the iterative scheme in the sense of Alghamdi et al. [The implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2014 (2014), Article ID 96, 9 pages] associated with Φ-hemicontractive mappings in a nonempty convex subset of an arbitrary Banach space. [ABSTRACT FROM AUTHOR]