Generalized g -quasivariational inequality

Rabia Nessah and Moussa Larbani

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-13

Abstract:

Suppose that X is a nonempty subset of a metric space E and Y is a nonempty subset of a topological vector space F . Let g : X → Y and ψ : X × Y → ℠be two functions and let S : X → 2 Y and T : Y → 2 F ∗ be two maps. Then the generalized g -quasivariational inequality problem (G g QVI) is to find a point x ¯ ∈ X and a point f ∈ T ( g ( x ¯ ) ) such that g ( x ¯ ) ∈ S ( x ¯ ) and sup y ∈ S ( x ¯ ) { Re ⠡ 〈 f , y − g ( x ¯ ) 〉 + ψ ( x ¯ , y ) } = ψ ( x ¯ , g ( x ¯ ) ) . In this paper, we prove the existence of a solution of (G g QVI).

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:497295

DOI: 10.1155/IJMMS.2005.3373

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