Proximal Point Algorithms for Finding Common Fixed Points of a Finite Family of Nonexpansive Multivalued Mappings in Real Hilbert Spaces

Document Type: Original Article

Author

School of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Durban, South Africa

10.22034/kjm.2019.88426

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, $F(J_{\lambda}^f\circ T_i) = F(J_{\lambda}^f)\cap F(T_i)=\Gamma.$ 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.

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