Geodesic
Viscosity approximation methods for the implicit midpoint rule of nonexpansive mappings in CAT(0) Spaces
Zhao, Liang-cai1 ; Chang, Shih-sen2 ; Wang, Lin3 ; Wang, Gang3
1 College of Mathematics, Yibin University, Yibin, Sichuan, 644007, China
2 Center for General Education, China Medical University, Taichung, 40402, Taiwan
3 College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 2, p. 386-394.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.010.02.05
Classification : 47H09, 47J25
Keywords: Viscosity, implicit midpoint rule, nonexpansive mapping, projection, variational inequality, CAT(0) space.

Zhao, Liang-cai 1 ; Chang, Shih-sen 2 ; Wang, Lin 3 ; Wang, Gang 3

1 College of Mathematics, Yibin University, Yibin, Sichuan, 644007, China
2 Center for General Education, China Medical University, Taichung, 40402, Taiwan
3 College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China 
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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 its applications, Tome 10 (2017) no. 2, p. 386-394. doi : 10.22436/jnsa.010.02.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.02.05/

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