Convergence analysis of generalized viscosity implicit rules for a nonexpansive semigroup with gauge functions :

Sunthrayuth, Pongsakorn ¹   ; Pakkaranang, Nuttapol ²   ; Kumam, Poom ³

¹ Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani, 12110, Thailand
² KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, 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
³ KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, 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;KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Facuty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 9, p. 1031-1044

Résumé

In this paper, we introduce an iterative algorithm for finding the set of common fixed points of nonexpansive semigroups by the generalized viscosity implicit rule in certain Banach spaces which has a uniformly Gateaux differentiable norm and admits the duality mapping $j_\varphi$, where $\varphi$ is a gauge function. We prove strong convergence theorems of proposed algorithm under appropriate conditions. As applications, we apply main result to solving the fixed point problems of countable family of nonexpansive mappings and the problems of zeros of accretive operators. Furthermore, we give some numerical examples for supporting our main results.

Détail

DOI : 10.22436/jnsa.011.09.02

Classification : 47H09, 47H10, 47J05, 47J25
Keywords: Nonexpansive semigroup, Banach spaces, strong convergence, fixed point problem, iterative method

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