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GENERAL VARIATIONAL INCLUSIONS AND GENERAL RESOLVENT EQUATIONS
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 Title & Authors
GENERAL VARIATIONAL INCLUSIONS AND GENERAL RESOLVENT EQUATIONS
Liu, Zeqing; Ume, Jeong-Sheok; Kang, Shin-Min;
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 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;
 Language
English
 Cited by
1.
ON GENERALIZED NONLINEAR QUASI-VARIATIONAL-LIKE INCLUSIONS DEALING WITH (h,η)-PROXIMAL MAPPING,;;;;

대한수학회지, 2008. vol.45. 5, pp.1323-1339 crossref(new window)
1.
Auxiliary principle for generalized nonlinear variational-like inequalities, International Journal of Mathematics and Mathematical Sciences, 2006, 2006, 1  crossref(new windwow)
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