Affiliation:
1. 1 Universite Amadou Mahtar Mbow , Dakar Senegal
Abstract
Abstract
We introduce a new iterative scheme by viscosity approximation method for finding a common point of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of multivalued quasi-nonexpansive mapping in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of multivalued quasi-nonexpansive. Futhermore, we applied our main result for finding a common solution of convex minimization problem and fixed points problem. Essentially a new approach for finding solutions of equilibrium problems and fixed point problems whith set-valued operators is provided.
Reference22 articles.
1. V. Berinde, M. Pacurar, The role of the Pompeiu-Hausdorff metric in fixed point theory, Creat. Math. Inform., vol. 22, no. 2, 2013, 143-150.
2. E. Blum, W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student, vol. 63, 1994, 123-145.
3. P. L. Combettes, S. A. Hirstoaga, Equilibrium programming in Hilbert spaces, Journal of Nonlinear and Convex Analysis, vol.6, no.1, 2005, 117-136.
4. P. Cholamjiak, W. Cholamjiak, S. Suantai, Viscosity approximation methods for nonexpansive multi-valued nonself mapping and equilibrium problem, Demon-stratio Mathematica, vol. XLVII, no. 2, 2014.
5. S. Chang, Y. Tang, L. Wang, G. Wang, Convergence theorems for some multi-valued generalized nonexpansive mappings, Fixed Point Theory and Applications, vol. 33, no. 1, 2014.