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

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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.

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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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Authors and Affiliations

  1. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, 152-8552, Japan

    W. Takahashi

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  1. W. Takahashi
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Correspondence to W. Takahashi.

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Communicated by J.-C. Yao.

The author is supported by Grant-in-Aid for Scientific Research No. 23540188 from Japan Society for the Promotion of Science.

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Takahashi, W. Strong Convergence Theorems for Maximal and Inverse-Strongly Monotone Mappings in Hilbert Spaces and Applications. J Optim Theory Appl 157, 781–802 (2013). https://doi.org/10.1007/s10957-012-0232-1

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  • DOI: https://doi.org/10.1007/s10957-012-0232-1

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