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

Abstract

In this paper by using the idea of mean convergence, we<br />introduce an iterative scheme for finding a common element of the<br />set of solutions of an equilibrium problem and the fixed points set<br />of a nonspreading-type mappings in Hilbert space. A strong<br />convergence theorem of the proposed iterative scheme is established<br />under some control conditions. The main result of this paper extend<br />the results obtained by Osilike and Isiogugu (Nonlinear Analysis 74<br />(2011) 1814-1822) and Kurokawa and Takahashi (Nonlinear Analysis 73<br />(2010) 1562-1568). We also give an example and numerical results are<br />also given.