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


Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand


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 74
(2011) 1814-1822) and Kurokawa and Takahashi (Nonlinear Analysis 73
(2010) 1562-1568). We also give an example and numerical results are
also given.