Generalized g-quasivariational inequality

Generalized g-quasivariational inequality

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→ℝ be two functions and let S:X→2Y and T:Y→2F∗ be two maps. Then the generalized g-quasivariational inequality problem (GgQVI) is to find a point x¯∈X and a point f∈...

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Main Authors: Rabia Nessah, Moussa Larbani
Format: Article
Language:English
Published: Hindawi Limited 2005-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/IJMMS.2005.3373
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spelling doaj-d403497e3b974558a077eb632c652aca2020-11-24T22:54:17ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005213373338510.1155/IJMMS.2005.3373Generalized g-quasivariational inequalityRabia Nessah0Moussa Larbani1ISTIT-LOSI (CNRS FRE 2732), Technology University of Troyes, 12 Rue Marie Curie, BP 2060, Troyes Cedex 10010, FranceDepartment of Business Administration, Faculty of Economics andManagement Sciences, International Islamic University Malaysia (IIUM), Jalan Gombak, Kuala Lumpur 53100, MalaysiaSuppose 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→ℝ be two functions and let S:X→2Y and T:Y→2F∗ be two maps. Then the generalized g-quasivariational inequality problem (GgQVI) is to find a point x¯∈X and a point f∈T(g(x¯)) such that g(x¯)∈S(x¯) and supy∈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 (GgQVI).http://dx.doi.org/10.1155/IJMMS.2005.3373
collection DOAJ
language English
format Article
sources DOAJ
author Rabia Nessah
Moussa Larbani
spellingShingle Rabia Nessah
Moussa Larbani
Generalized g-quasivariational inequality
International Journal of Mathematics and Mathematical Sciences
author_facet Rabia Nessah
Moussa Larbani
author_sort Rabia Nessah
title Generalized g-quasivariational inequality
title_short Generalized g-quasivariational inequality
title_full Generalized g-quasivariational inequality
title_fullStr Generalized g-quasivariational inequality
title_full_unstemmed Generalized g-quasivariational inequality
title_sort generalized g-quasivariational inequality
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2005-01-01
description 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→ℝ be two functions and let S:X→2Y and T:Y→2F∗ be two maps. Then the generalized g-quasivariational inequality problem (GgQVI) is to find a point x¯∈X and a point f∈T(g(x¯)) such that g(x¯)∈S(x¯) and supy∈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 (GgQVI).
url http://dx.doi.org/10.1155/IJMMS.2005.3373
work_keys_str_mv AT rabianessah generalizedgquasivariationalinequality
AT moussalarbani generalizedgquasivariationalinequality
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