Abstract
We prove a fixed point theorem for generalized asymptotic pointwise nonexpansive mapping in the setting of a hyperbolic space. A one-step iterative scheme approximating common fixed point of two generalized asymptotic pointwise (quasi-) nonexpansive mappings in this setting is provided. We obtain $\triangle -$convergence and strong convergence theorems of the iterative scheme for two generalized asymptotic pointwise nonexpansive mappings in the same setting. Our results generalize and extend some related results in the literature.
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