Geodesic
Strong and weak convergence theorems for split equilibrium problems and fixed point problems in Banach spaces
Guo, Baohua1 ; Ping, Ping1 ; Zhao, Haiqing1 ; Cho, Yeol Je2
1 Department of Mathematics and physics, North China Electric Power University, Baoding 071003, China
2 Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 660-701, Korea;Center for General Education, China Medical University, Taichung 40402, Taiwan
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 6, p. 2886-2901.

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

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
DOI : 10.22436/jnsa.010.06.04
Classification : 47H05, 47H09
Keywords: Split equilibrium problem, equilibrium problem, fixed point

Guo, Baohua 1 ; Ping, Ping 1 ; Zhao, Haiqing 1 ; Cho, Yeol Je 2

1 Department of Mathematics and physics, North China Electric Power University, Baoding 071003, China
2 Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 660-701, Korea;Center for General Education, China Medical University, Taichung 40402, Taiwan 
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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 its applications, Tome 10 (2017) no. 6, p. 2886-2901. doi : 10.22436/jnsa.010.06.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.06.04/

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