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http://dx.doi.org/10.4134/BKMS.2004.41.2.241

GENERAL VARIATIONAL INCLUSIONS AND GENERAL RESOLVENT EQUATIONS

Liu, Zeqing (Department of Mathematics, Liaoning Normal University)
Ume, Jeong-Sheok (Department of Applied Mathematics, Changwon National University)
Kang, Shin-Min (Department of Mathematics And Research Institute of Natural Science, Gyeongsang National University)

Publication Information

Bulletin of the Korean Mathematical Society / v.41, no.2, 2004 , pp. 241-256 More about this Journal

Abstract

In this paper, we introduce and study a new class of variational inclusions, called the general variational inclusion. We prove the equivalence between the general variational inclusions, the general resolvent equations, and the fixed-point problems, using the resolvent operator technique. This equivalence is used to suggest and analyze a few iterative algorithms for solving the general variational inclusions and the general resolvent equations. Under certain conditions, the convergence analyses are also studied. The results presented in this paper generalize, improve and unify a number of recent results.

Keywords

general variational inclusion; general resolvent equation; relaxed Lipschitz mapping; relaxed monotone mapping;

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Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

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