Proximal Point Algorithms for Finding Common Fixed Points of a Finite Family of Nonexpansive Multivalued Mappings in Real Hilbert Spaces
Akindele Adebayo Mebawondu · Khayyam journal of mathematics · 2019
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, $F(J_{lambda}^fcirc T_i) = F(J_{lambda}^f)cap F(T_i)=Gamma.$ 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.