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Topological KKM theorems and generalized vector equilibria on G-convex spaces with applications

Authors: El Mostafa Kalmoun and Hassan Riahi
Journal: Proc. Amer. Math. Soc. 129 (2001), 1335-1348
MSC (1991): Primary 49J35, 54H25; Secondary 54Cxx, 52A01
Published electronically: January 8, 2001
MathSciNet review: 1814159
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In the present paper, slightly modifying the topological KKM Theorem of Park and Kim (1996), we obtain a new existence theorem for generalized vector equilibrium problems related to an admissible multifunction. We work here under the general framework of G-convex space which does not have any linear structure. Also, we give applications to greatest element, fixed point and vector saddle point problems. The results presented in this paper extend and unify many results in the literature by relaxing the compactness, the closedness and the convexity conditions.

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Additional Information

El Mostafa Kalmoun
Affiliation: Faculté des Sciences I Semlalia, Mathématiques, Université Cadi Ayyad, B.P. 2390, Marrakech 40000, Morocco

Hassan Riahi
Affiliation: Faculté des Sciences I Semlalia, Mathématiques, Université Cadi Ayyad, B.P. 2390, Marrakech 40000, Morocco

Keywords: KKM theorem, vector equilibria, G-convex space, generalized G-convexity, admissible multifunctions, transfer closedness, pseudomonotonicity, greatest element, fixed point, vector saddle point
Received by editor(s): July 9, 1999
Published electronically: January 8, 2001
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2001 American Mathematical Society

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