Document Type : Research Paper

Authors

• U. Singthong
• S. Suntai

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

Abstract

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.

Keywords

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