Abstract
In this paper, we introduce a new three-step iteration scheme and establish convergence results for the approximation of fixed points of asymptotically quasi-nonexpansive mapping in the framework of CAT(0) space and also give an example of a nonlinear function that is asymptotically quasi-nonexpansive but it is not quasi-nonexpansive. Finally, we display the efficiency of the proposed scheme compared to different iterative schemes by a numerical example in the literature. Our results generalize and improve many well-known results in the literature of iterations in fixed point theory.
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