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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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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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