Modified viscosity type iteration for total asymptotically nonexpansive mappings in CAT(0) spaces and its application to optimization problems
Volume 11, Issue 2, pp 288--302
http://dx.doi.org/10.22436/jnsa.011.02.10
Publication Date: February 07, 2018
Submission Date: October 22, 2017
Revision Date: November 26, 2017
Accteptance Date: December 01, 2017
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Authors
Wiyada Kumam
- Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Thanyaburi, Pathumthani 12110, Thailand.
Nuttapol Pakkaranang
- 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.
Poom Kumam
- 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.
Abstract
In this paper, we introduce a modified two-step viscosity iteration process for total asymptotically nonexpansive mappings in CAT(0) spaces. We prove strong convergence of the proposed iteration process to a fixed point of total asymptotically nonexpansive mappings in CAT(0) spaces, which also shows that the limit of the sequence generated by proposed iteration process solves the solution of the variational inequality. We also provide illustrating a numerical example for supporting our main results. Moreover, we show the existence of solutions of our consequently results for some applications.
Share and Cite
ISRP Style
Wiyada Kumam, Nuttapol Pakkaranang, Poom Kumam, Modified viscosity type iteration for total asymptotically nonexpansive mappings in CAT(0) spaces and its application to optimization problems, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 2, 288--302
AMA Style
Kumam Wiyada, Pakkaranang Nuttapol, Kumam Poom, Modified viscosity type iteration for total asymptotically nonexpansive mappings in CAT(0) spaces and its application to optimization problems. J. Nonlinear Sci. Appl. (2018); 11(2):288--302
Chicago/Turabian Style
Kumam, Wiyada, Pakkaranang, Nuttapol, Kumam, Poom. "Modified viscosity type iteration for total asymptotically nonexpansive mappings in CAT(0) spaces and its application to optimization problems." Journal of Nonlinear Sciences and Applications, 11, no. 2 (2018): 288--302
Keywords
- Viscosity approximation methods
- total asymptotically nonexpansive mapping
- variational inequality
- CAT(0) spaces
MSC
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