Proximal Point Algorithm for a Common of Countable Families of Inverse Strongly Accretive Operators and Nonexpansive Mappings with Convergence Analysis
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT) 126 Pracha-Uthit Road, Bang Mod, 10140 Thung Khru, Bangkok, Thailand
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT) 126 Pracha-Uthit Road, Bang Mod, 10140 Thung Khru, Bangkok, Thailand; Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of North Bangkok (KMUTNB) 1518 Pracharat 1 Road, Wongsawang, 10800 Bangsue, Bangkok, Thailand
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT) 126 Pracha-Uthit Road, Bang Mod, 10140 Thung Khru, Bangkok, 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, 10140 Thung Khru, Bangkok, Thailand; China Medical University No. 91, Hsueh-Shih Road, 40402 Taichung, Taiwan
In this paper, we investigate and analyze a proximal point algorithm via viscosity approximation method with error. This algorithm is introduced for finding a common zero point for a countable family of inverse strongly accretive operators and a countable family of nonexpansive mappings in Banach spaces. Our result can be extended to some well known results from a Hilbert space to a uniformly convex and 2−uniformly smooth Banach space. Finally, we establish the strong convergence theorems for the proximal point algorithm. Also, some illustrative numerical examples are presented.
Promluang, K., Sitthithakerngkiet, K., & Kumam, P. (2016). Proximal Point Algorithm for a Common of Countable Families of Inverse Strongly Accretive Operators and Nonexpansive Mappings with Convergence Analysis. Mathematical Modelling and Analysis, 21(1), 95-118. https://doi.org/10.3846/13926292.2016.1137090
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