@article { author = {Mebawondu, Akindele}, title = {Proximal Point Algorithms for Finding Common Fixed Points of a Finite Family of Nonexpansive Multivalued Mappings in Real Hilbert Spaces}, journal = {Khayyam Journal of Mathematics}, volume = {5}, number = {2}, pages = {113-123}, year = {2019}, publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)}, issn = {2423-4788}, eissn = {2423-4788}, doi = {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.}, keywords = {Proximal point algorithms,fixed point,multivalued nonexpansive mapping,Hilbert space}, url = {https://www.kjm-math.org/article_88426.html}, eprint = {https://www.kjm-math.org/article_88426_f7ea9c7dc575d3815a88a6312c349e52.pdf} }