Abstract
Fixed points of monotone α -nonexpansive and generalized β -nonexpansive mappings have been approximated in Banach space. Our purpose is to approximate the fixed points for the above mappings in hyperbolic space. We prove the existence and convergence results using some iteration processes.
Highlights
In 1965, Browder [1], Göhde [2], and Kirk [3] started working in the approximation of fixed point for nonexpansive mappings
Browder obtained fixed point theorem for nonexpansive mapping on a subset of a Hilbert space that is closed bounded and convex
Browder [1] and Göhde [2] generalized the same result from a Hilbert space to a uniformly convex Banach space
Summary
In 1965, Browder [1], Göhde [2], and Kirk [3] started working in the approximation of fixed point for nonexpansive mappings. Browder obtained fixed point theorem for nonexpansive mapping on a subset of a Hilbert space that is closed bounded and convex. Dehici and Najeh [4] and Tan and Cho [5] approximated fixed point result for nonexpansive mappings in Banach space and Hilbert space. Song et al [8] extended the notion of α-nonexpansive mapping to monotone α-nonexpansive mapping in order Banach spaces and obtained some existence and convergence theorem for the Mann iteration (see [9] and the reference therein).
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