Further investigation into approximation of a common solution of fixed point problems and split feasibility problems

The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set Ω of the split feasibility problem and the set F(T) of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of p-uniformly convex Banach spaces which are also uniformly smooth. By combining Mann's iterative method and the Halpern's approximation method, we propose an iterative algorithm for finding an element of the set F(T)⋂ Ω; moreover, we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method. Our results extend and complement many known related results in the literature.