Viscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mapping in complete CAT(0) spaces
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Authors
Yi Li
- School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China.
Hongbo Liu
- School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China.
Abstract
In this paper, the implicit midpoint rule of asymptotically nonexpansive mapping in CAT(0) spaces is introduced. By the
viscosity approximation method, we prove that the proposed implicit iteration converges strongly to a fixed point of asymptotically
nonexpansive mapping under certain assumptions imposed on the sequence of parameters. The results presented in the
paper improve and extend various results in the existing literature.
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ISRP Style
Yi Li, Hongbo Liu, Viscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mapping in complete CAT(0) spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 3, 1270--1280
AMA Style
Li Yi, Liu Hongbo, Viscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mapping in complete CAT(0) spaces. J. Nonlinear Sci. Appl. (2017); 10(3):1270--1280
Chicago/Turabian Style
Li, Yi, Liu, Hongbo. "Viscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mapping in complete CAT(0) spaces." Journal of Nonlinear Sciences and Applications, 10, no. 3 (2017): 1270--1280
Keywords
- viscosity approximation methods
- complete CAT(0) space
- \(\Delta\)-convergence
- Asymptotically nonexpansive
- implicit iteration.
MSC
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