Abstract: In this paper, we introduce and study an iterative approximation method for finding a common element of the set of fixed points of multi valued hemicontractive-type mapping,  the set of solutions of split equilibrium problem and the set of solutions of variational inequality problem for continuous monotone mapping in real Hilbert spaces. Furthermore, we proved strong convergence theorem for the sequences generated by the proposed iterative algorithm under some conditions imposed on parameters. Our results improve and generalize most of the results that have been previously proved by some authors recently.

Key words: Demiclosedness principle, Fixed point problem, hemicontractive-type multi-valued mapping, split equilibrium problem, variational inequality problem. 

How to cite this article:

Tesfalem Hadush Meche and Habtu Zegeye, Approximation of Common Solutions of Fixed Point Problem for Hemicontractive-type Mapping, Split Equilibrium and Variational Inequality Problems, International Journal of Advances in Mathematics, Volume 2017, Number 5, Pages 70-89, 2017.