4. Strong Convergence Analysis For Fixed Point, Variational Inequality And Equilibrium Problems In Hilbert Spaces

By Francis Monday Nkwuda
Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria

Abstract
In this paper, we introduce and study strong convergence analysis for finding a common element of the set of fixed points of asymptotically nonexpansive mapping, the set of solutions of generalized mixed equilibrium problem and the set of solutions of variational inequality problem. We prove that the sequence generated converges strongly to the common element of the three aforementioned problems. Furthermore, an optimization problem is solved using the theorems in real Hilbert spaces.

Keywords: Inverse strongly monotone mapping, asymptotically nonexpansive mapping, equilibrium problem, Hilbert space.
2010hematics Subject Classification: 47H09; 47H10; 49J20; 49J40.