Equilibrium problems and fixed point problems for nonspreading-type mappings in hilbert space

In this paper by using the idea of mean convergence, we introduce an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the fixed points set of a nonspreading-type mappings in Hilbert space. A strong convergence theorem of the proposed iterative scheme is established under some control conditions. The main result of this paper extend the results obtained by Osilike and Isiogugu (Nonlinear Analysis ۷۴ (۲۰۱۱) ۱۸۱۴-۱۸۲۲) and Kurokawa and Takahashi (Nonlinear Analysis ۷۳ (۲۰۱۰) ۱۵۶۲-۱۵۶۸). We also give an example and numerical results arealso given.

Keywords:

k-strictly pseudononspreading mappings , nonspreading mappings , fixed points , strong convergence , equilibrium problem , Hilbert spaces