Zegeye, Habtu(Professor)Hadush, Tesfalem2018-07-192023-11-042018-07-192023-11-042017-04http://etd.aau.edu.et/handle/123456789/9298Many of the most important problems arising in nonlinear analysis reduce to solving a given equation, which in turn may be reduced to finding the fixed points of a certain mapping or solutions of varia- tional inequality and equilibrium problems. Because of the relation between the fixed point problem, variational inequality and equilib- rium problems, finding common solutions of these problems is an important field of research. In this thesis, we introduce and study an iterative algorithm which converges strongly to a common element of the set of xed points of a more general class of Lipschitz hemicontractive-type multi-valued mappings and the set of solutions of variational inequality problem in real Hilbert spaces. In addition, we have obtained strong convergence theorems of an iterative process for finding a common solution of the fixed point problem for Lipschitz hemicontractive-type multi-valued mapping and the generalized equilibrium problem in the framework of real Hilbert spaces. We also extend this result to a finite family of generalized equilibrium problems. Furthermore, a viscosity-type approximation method is introduced for approximating a common element of the set of fixed points of a nonexpansive multi-valued mapping, the sets of solutions of a split equilibrium and a variational inequality problems.enApproximating CommonSolutions of VariationalThesis