Korean J. Math. Vol. 28 No. 4 (2020) pp.915-929
DOI: https://doi.org/10.11568/kjm.2020.28.4.915

Common fixed point of generalized asymptotic pointwise (quasi-) nonexpansive mappings in hyperbolic spaces

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Published: Dec 30, 2020
Keywords:
Hyperbolic Space, Delta-convergence, strong convergence, common fixed point, one-step iterations
Mathematics Subject Classification:
47H09, 47H10, 47J25

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Khairul Saleh
Department of Mathematics and Statistics King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia
Hafiz Fukhar-ud-din
Department of Mathematics The Islamia University of Bahawalpur Bahawalpur 63100, Pakistan

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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