Dynamical technique for split common fixed point problem in Banach spaces

We study the split common fixed point problem for Bregman demigeneralized type mappings in the context of two real Banach spaces. We propose a new self-adaptive method and prove that it converges strongly to a solution of this problem. As consequences of our results, we propose some new self-adaptive methods for solving split feasibility problem, split common null point problem and split equilibrium problem, using some dynamical stepsize techniques, which allow these methods to be easily implemented without prior knowledge of the norm of the bounded linear operator. We perform some numerical experiments to demonstrate implementation and efficiency of our methods.

Automated summary

This article studies the split common fixed point problem for Bregman demigeneralized type mappings in the context of two real Banach spaces. A new self-adaptive method is proposed and proven to strongly converge to a solution of this problem. As a consequence, new self-adaptive methods for solving split feasibility problem, split common null point problem, and split equilibrium problem are proposed using dynamical stepsize techniques, allowing these methods to be easily implemented without prior knowledge of the norm of the bounded linear operator. Numerical experiments are performed to demonstrate the implementation and efficiency of the methods.