The purpose of this paper is to investigate convergence of a hybrid Halpern process for fixed point and equilibrium problems. Strong convergence theorems of common solutions are established in a strictly convex and uniformly smooth Banach space which also has the Kadec-Klee property.

The purpose of this paper is to investigate fixed points of an asymptotically quasi-φ-nonexpansive mapping in the intermediate sense and a bifunction equilibrium problem. We obtain a strong convergence theorem of solutions in the framework of Banach spaces.