On strong and \(\Delta\)-convergence of modified S-iteration for uniformly continuous total asymptotically nonexpansive mappings in \(CAT(\kappa)\) spaces


Authors

Plern Saipara - Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand. Parin Chaipunya - Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand. Yeol Je Cho - Department of Mathematics Education, Gyeongsang Natoinal University, Jinju 660-701, Korea. Poom Kumam - Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand. - Theoretical and Computational Science (TaCS) Center, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.


Abstract

In this paper, we obtain strong and \(\Delta\)-convergence theorems of modified S-iteration for total asymptotically nonexpansive mappings in \(CAT(\kappa)\) spaces with \(\kappa > 0\). Our results extend and improve the corresponding recent results announced by Panyanak [B. Panyanak, J. Inequal. Appl., 2014 (2014), 13 pages] and many authors.


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