Strong and weak convergence theorems for split equilibrium problems and fixed point problems in Banach spaces
Baohua Guo, Ping Ping, Haiqing Zhao, Yeol Je Cho · The Journal of Nonlinear Sciences and Applications · 2017
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