Viscosity approximation methods for the implicit midpoint rule of nonexpansive mappings in CAT(0) Spaces


Authors

Liang-cai Zhao - College of Mathematics, Yibin University, Yibin, Sichuan, 644007, China. Shih-sen Chang - Center for General Education, China Medical University, Taichung, 40402, Taiwan. Lin Wang - College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China. Gang Wang - College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China.


Abstract

The purpose of this paper is to introduce the implicit midpoint rule of nonexpansive mappings in CAT(0) spaces. The strong convergence of this method is proved under certain assumptions imposed on the sequence of parameters. Moreover, it is shown that the limit of the sequence generated by the implicit midpoint rule solves an additional variational inequality. Applications to nonlinear Volterra integral equations and nonlinear variational inclusion problem are included. The results presented in the paper extend and improve some recent results announced in the current literature.


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ISRP Style

Liang-cai Zhao, Shih-sen Chang, Lin Wang, Gang Wang, Viscosity approximation methods for the implicit midpoint rule of nonexpansive mappings in CAT(0) Spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 386--394

AMA Style

Zhao Liang-cai, Chang Shih-sen, Wang Lin, Wang Gang, Viscosity approximation methods for the implicit midpoint rule of nonexpansive mappings in CAT(0) Spaces. J. Nonlinear Sci. Appl. (2017); 10(2):386--394

Chicago/Turabian Style

Zhao, Liang-cai, Chang, Shih-sen, Wang, Lin, Wang, Gang. "Viscosity approximation methods for the implicit midpoint rule of nonexpansive mappings in CAT(0) Spaces." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 386--394


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