On Fixed Point Results for Finite Families of Alpha-Hemicontractive Mappings, Variationa lnequality Problems and Split Equilibrium Problems

ln this paper, we introduce an iterative scheme for approximating a common element of the fixed point sets of a finite family of a multivalued -hemicontractive mappings, the set of solutions of a finite family of variational inequality problems and the set of solutions of a finite family of equilibrium problems. Using our scheme, we establish strong convergence theorems of the aforementioned problems in the framework of real Hilbert spaces. Our results improve, extend, generalise and unify many recent results in this direction.

Keywords:

Split equilibrium problem , variational inequality problem , Alpha-hemicontractive mapping , iterative approximation , strong convergence , xed point , nite family , Hilbert space.