Convergence theorem for fixed point and split generalized variational inclusion problems with multiple output sets in Banach spaces

In the framework of p-uniformly convex uniformly and smooth Banach spaces, we introduce the split common generalized variational incusion problem with multiple output sets. Using a Halpern iterative method, we propose a strong convergence algorithm for approximating a common solution of this problem and fixed point of a Bregman firmly nonexpansive mapping. Furthermore, we give a theoretical application to split common minimization problem with multiple output sets. We also report some numerical examples to illustrate the performance of our proposed method.