Article ID: | iaor20132856 |
Volume: | 157 |
Issue: | 3 |
Start Page Number: | 781 |
End Page Number: | 802 |
Publication Date: | Jun 2013 |
Journal: | Journal of Optimization Theory and Applications |
Authors: | Takahashi W |
Keywords: | Hilbert space, mapping |
In this paper, we prove two strong convergence theorems for finding a common point of the set of zero points of the addition of an inverse‐strongly monotone mapping and a maximal monotone operator and the set of zero points of a maximal monotone operator, which is related to an equilibrium problem in a Hilbert space. Such theorems improve and extend the results announced by Y. Liu (Nonlinear Anal. 71:4852–4861, 2009). As applications of the results, we present well‐known and new strong convergence theorems which are connected with the variational inequality, the equilibrium problem and the fixed point problem in a Hilbert space.