Solving Split Mixed Equilibrium With Multiple Output Sets and Fixed Point of Certain Multi-Valued Mappings

In this paper, we study the split mixed equilibrium problem which includes the equilibrium problem, split convex minimization problem and split equilibrium problem, to mention a few. In addition, we propose a Halpern iterative method for solving split mixed equilibrium problem with multiple output sets and fixed point of a finite family of multi-valued strictly pseudo-contractive mappings in the framework of real Hilbert spaces. We prove a strong convergence theorem without imposing any compactness condition. Lastly, we present some consequences and give applications of our main result to split mixed variational inequality and split convex minimization problems. The result discussed in this article extends and complements many related results in literature.