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

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

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Article ID: iaor20132856
Volume: 157
Issue: 3
Start Page Number: 781
End Page Number: 802
Publication Date: Jun 2013
Journal: Journal of Optimization Theory and Applications
Authors:
Keywords: Hilbert space, mapping
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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