Implicit iterative algorithms of the split common fixed point problem for Bregman quasi-nonexpansive mapping in Banach spaces

In this paper,we study a modified implicit rule for finding a solution of split common fixed point problem of a Bregman quasi-nonexpansive mapping in Banach spaces.We propose a new iterative algorithm and prove the strong convergence theorem under appropriate conditions.As an application,the results are applied to solving the zero problem and the equilibrium problem.