Existence Theorem for the Discontinuous Generalized Quasivariational Inequality Problem

P. Cubiotti
Additional contact information
P. Cubiotti: University of Messina

Journal of Optimization Theory and Applications, 2003, vol. 119, issue 3, No 10, 623-633

Abstract: Abstract We consider the following generalized quasivariational inequality problem: given a real Banach space E with topological dual E* and given two multifunctions G:X→2 X and F:X→2 E *, find $$(\hat x,\hat \varphi ) \in X \times E*$$ such that $$\hat x \in G(\hat x),{\text{ }}\hat \varphi \in F(\hat x),{\text{ }}\left\langle {\hat \varphi ,\hat x - y} \right\rangle \leqslant 0,{\text{ for all }}y \in G(\hat x).$$ We prove an existence theorem where F is not assumed to have any continuity or monotonicity property. Making use of a different technical construction, our result improves some aspects of a recent existence result (Theorem 3.1 of Ref. 1). In particular, the coercivity assumption of this latter result is weakened meaningfully.

Keywords: Generalized quasivariational inequalities; affine hulls; lower semicontinuity; Hausdorff lower semicontinuity; fixed points (search for similar items in EconPapers)
Date: 2003
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1023/B:JOTA.0000006960.70743.63 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:119:y:2003:i:3:d:10.1023_b:jota.0000006960.70743.63

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1023/B:JOTA.0000006960.70743.63

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().