Journal
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Volume 157, Issue 3, Pages 781-802Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-012-0232-1
Keywords
Equilibrium problem; Fixed point; Inverse-strongly monotone mapping; Maximal monotone operator; Resolvent; Strict pseudo-contraction
Funding
- Japan Society for the Promotion of Science [23540188]
- Grants-in-Aid for Scientific Research [23540188] Funding Source: KAKEN
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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.
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