Solving the Split Feasibility Problem and the Fixed Point Problem of Left Bregman Firmly Nonexpansive Mappings via the Dynamical Step Sizes in Banach Spaces

Abstract

In this work, we suggest a new self-adaptive method using the dynamical step size technique for solving the split feasibility problem and the fixed point problem of left Bregman firmly nonexpansive mappings in a certain Banach space. We establish the strong convergence without the computation of the operator norms. Finally, we give some examples including its numerical experiments to show the efficiency and the implementation of our proposed method.