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Strong Convergence Theorems for Maximal and Inverse-Strongly Monotone Mappings in Hilbert Spaces and Applications

  • W. Takahashi
Article

Abstract

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.

Keywords

Equilibrium problem Fixed point Inverse-strongly monotone mapping Maximal monotone operator Resolvent Strict pseudo-contraction 

Notes

Acknowledgements

The author would like to express his appreciation to Professor Jen-Chih Yao for useful suggestions that improved the content of this manuscript.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyTokyoJapan

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