PROXIMAL POINT ALGORITHMS FOR FINDING COMMON FIXED POINTS OF A FINITE FAMILY OF NONEXPANSIVE MULTIVALUED MAPPINGS IN REAL HILBERT SPACES

Abstract

We start by showing that the composition of fixed point of minimization problem and a finite family of multivalued nonexpansive mapping are equal to the common solution of the fixed point of each of the aforementioned problems, that is, F(J f λ ◦ Ti) = F(J f λ ) ∩ F(Ti) = Γ. Furthermore, we then propose an iterative algorithm and prove weak and strong convergence results for approximating the common solution of the minimization problem and fixed point problem of a multivalued nonexpansive mapping in the framework of real Hilbert space. Our result extends and complements some related results in literature.