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

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.