Strong and weak convergence theorems for split equilibrium problems and fixed point problems in Banach spaces


Authors

Baohua Guo - Department of Mathematics and physics, North China Electric Power University, Baoding 071003, China. Ping Ping - Department of Mathematics and physics, North China Electric Power University, Baoding 071003, China. Haiqing Zhao - Department of Mathematics and physics, North China Electric Power University, Baoding 071003, China. Yeol Je Cho - Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 660-701, Korea. - Center for General Education, China Medical University, Taichung 40402, Taiwan.


Abstract

In this paper, we give some strong and weak convergence algorithms to find a common element of the solution set of a split equilibrium problem and the fixed point set of a relatively nonexpansive mapping in Banach spaces. Our algorithms only involve the operator \(A\) itself and do not need any conditions of the adjoint operator \(A^*\) of \(A\) and the norm \(\|A\|\) of \(A\) which are different from the other results in the literature. By applying our main results, we show the existence of a solution of a split feasibility problem in Banach spaces. Finally, we give an example to illustrate the main results of this paper


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ISRP Style

Baohua Guo, Ping Ping, Haiqing Zhao, Yeol Je Cho, Strong and weak convergence theorems for split equilibrium problems and fixed point problems in Banach spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 6, 2886--2901

AMA Style

Guo Baohua, Ping Ping, Zhao Haiqing, Cho Yeol Je, Strong and weak convergence theorems for split equilibrium problems and fixed point problems in Banach spaces. J. Nonlinear Sci. Appl. (2017); 10(6):2886--2901

Chicago/Turabian Style

Guo, Baohua, Ping, Ping, Zhao, Haiqing, Cho, Yeol Je. "Strong and weak convergence theorems for split equilibrium problems and fixed point problems in Banach spaces." Journal of Nonlinear Sciences and Applications, 10, no. 6 (2017): 2886--2901


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