Viscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mappings in Hilbert spaces
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Authors
Liang-Cai Zhao
- College of Mathematics, Yibin University, Yibin, Sichuan, 644007, P. R. China.
Shih-Sen Chang
- Center for General Education, China Medical University, Taichung, 40402, Taiwan.
Ching-Feng Wen
- Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung, 80708, Taiwan.
Abstract
The purpose of this paper is to introduce the implicit midpoint rule of asymptotically nonexpansive
mappings in Hilbert spaces. The strong convergence of this viscosity method is proved under certain assumptions
imposed on the sequence of parameters. Moreover, it is shown that the limit solves an additional
variational inequality. Applications to nonlinear variational inclusion problem, nonlinear Volterra integral
equations, variational inequality problem and hierarchical minimization problems are included. The results
presented in the paper extend and improve some recent results announced in the current literature.
Share and Cite
ISRP Style
Liang-Cai Zhao, Shih-Sen Chang, Ching-Feng Wen, Viscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mappings in Hilbert spaces, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4478--4488
AMA Style
Zhao Liang-Cai, Chang Shih-Sen, Wen Ching-Feng, Viscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mappings in Hilbert spaces. J. Nonlinear Sci. Appl. (2016); 9(6):4478--4488
Chicago/Turabian Style
Zhao, Liang-Cai, Chang, Shih-Sen, Wen, Ching-Feng. "Viscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mappings in Hilbert spaces." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4478--4488
Keywords
- Viscosity
- implicit midpoint rule
- asymptotically nonexpansive mapping
- projection
- variational inequality.
MSC
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