A new self-adaptive simultaneous algorithm for split equality variational inclusion and fixed point problems in real Banach spaces

In this work, we study the split equality variational inclusion and fixed point problems involving Bregman weakly relatively nonexpansive mappings in p-uniformly convex and uniformly smooth real Banach spaces. This research expands upon the current findings that are limited to Hilbert spaces or 2-uniformly convex Banach spaces. We introduce a new simultaneous algorithm with an inertial term to accelerate the rate of convergence of this algorithm and a self-adaptive technique, which is independent of the Lipschitz constant, to approximate a common solution to these problems. This helps to improve the convergence of the method while weakening the conditions on the problem used in existing methods. We also provided some numerical experiments to illustrate the efficiency and accuracy of the method with the non-inertial version.