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

W. Takahashi ()
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W. Takahashi: Tokyo Institute of Technology

Journal of Optimization Theory and Applications, 2013, vol. 157, issue 3, No 11, 802 pages

Abstract: 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 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-012-0232-1

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