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http://dx.doi.org/10.7858/eamj.2013.022

A PROXIMAL POINT ALGORITHM FOR SOLVING THE GENERAL VARIATIONAL INCLUSIONS WITH M(·, ·)-MONOTONE OPERATORS IN BANACH SPACES  

Chen, Junmin (College of Mathematics and Computer, Hebei University)
Wang, Xian (College of Mathematics and Computer, Hebei University)
He, Zhen (College of Mathematics and Computer, Hebei University)
Publication Information
East Asian mathematical journal / v.29, no.3, 2013 , pp. 315-326 More about this Journal
Abstract
In this paper, a new monotonicity, $M({\cdot},{\cdot})$-monotonicity, is introduced in Banach spaces, and the resolvent operator of an $M({\cdot},{\cdot})$-monotone operator is proved to be single valued and Lipschitz continuous. By using the resolvent operator technique associated with $M({\cdot},{\cdot})$-monotone operators, we construct a proximal point algorithm for solving a class of variational inclusions. And we prove the convergence of the sequences generated by the proximal point algorithms in Banach spaces. The results in this paper extend and improve some known results in the literature.
Keywords
General variational inclusion; Maximal monotone mapping; $M({\cdot},{\cdot})$-monotone operator; Generalized resolvent operator;
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