Approximation of common solutions of fixed point problem for α-hemicontractive mapping, split equilibrium and variational inequality problems

Abstract

ln this paper, a Halpern-type algorithm for approximating a common fixed point of multivalued α-hemicontractive mappings and a set of solutions of split equilibrium and variational inequality problems is constructed. Strong convergence of the sequence generated by the algorithm is proved in the setting real Hilbert spaces. Our results improved and generalised the results of Meche and Zegeye [2] in particular and some recent results in Literature.