Cloud hybrid methods for solving split equilibrium and fixed point problems for a family of countable quasi-Lipschitz mappings and applications
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Authors
Yongchun Xu
- Department of Mathematics, College of Science, Hebei North University, Zhangjiakou 075000, China.
Yanxia Tang
- Department of Mathematics, College of Science, Hebei North University, Zhangjiakou 075000, China.
Jinyu Guan
- Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China.
Yongfu Su
- Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China.
Abstract
The purpose of this article is to introduce a new multidirectional hybrid shrinking projection iterative algorithm (or called
cloud hybrid shrinking projection iterative algorithm) for solving the common element problems which consist of a generalized
split equilibrium problems and fixed point problems for a family of countable quasi-Lipschitz mappings in the framework of
Hilbert spaces. It is proved that under appropriate conditions, the sequence generated by the multidirectional hybrid shrinking
projection method, converges strongly to some point which is the common fixed point of a family of countable quasi-Lipschitz
mappings and the solution of the generalized split equilibrium problems. This iteration algorithm can accelerate the convergence
speed of iterative sequence. The main results were also applied to solve split variational inequality problem and split optimization
problems. Meanwhile, the main results were also used for solving common problems which consist of a generalized split
equilibrium problems and fixed point problems for asymptotically nonexpansive mappings. The results of this paper improve
and extend the previous results given in the literature.
Share and Cite
ISRP Style
Yongchun Xu, Yanxia Tang, Jinyu Guan, Yongfu Su, Cloud hybrid methods for solving split equilibrium and fixed point problems for a family of countable quasi-Lipschitz mappings and applications, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 752--770
AMA Style
Xu Yongchun, Tang Yanxia, Guan Jinyu, Su Yongfu, Cloud hybrid methods for solving split equilibrium and fixed point problems for a family of countable quasi-Lipschitz mappings and applications. J. Nonlinear Sci. Appl. (2017); 10(2):752--770
Chicago/Turabian Style
Xu, Yongchun, Tang, Yanxia, Guan, Jinyu, Su, Yongfu. "Cloud hybrid methods for solving split equilibrium and fixed point problems for a family of countable quasi-Lipschitz mappings and applications." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 752--770
Keywords
- Hybrid shrinking projection
- split equilibrium problem
- fixed point
- quasi-Lipschitz mapping
- split variational inequality
- split optimization problem.
MSC
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