Existence Results for Variational Inequalities with Surjectivity Consequences Related to Generalized Monotone Operators

Gábor Kassay () and Mihaela Miholca ()
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Gábor Kassay: Babes-Bolyai University
Mihaela Miholca: Babes-Bolyai University

Journal of Optimization Theory and Applications, 2013, vol. 159, issue 3, No 11, 740 pages

Abstract: Abstract We present existence results for variational inequalities given by generalized monotone operators. As a consequence, we deduce the existence of zeros, or even more, the surjectivity of some classes of set-valued operators. We show that by strengthening the continuity assumptions, similar surjectivity results can be obtained without any monotonicity assumption. In the framework of reflexive Banach spaces, we extend a related result due to Inoan and Kolumbán (Nonlinear Anal. 68:47–53, 2008).

Keywords: Equilibrium problem; Variational inequality; Quasicoercive operator; Properly quasimonotone operator; F-hemicontinuity; C-pseudomonotone operator (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-013-0383-8

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