An Ekeland's variational principle for set-valued mappings with applications

• Autores: J. Zeng, S. J. Li
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 230, Nº 2, 2009, págs. 477-484
• Idioma: inglés
• DOI: 10.1016/j.cam.2008.12.014
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• Resumen

  • In this paper, we obtain a general Ekeland�s variational principle for set-valued mappings in complete metric space, which is different from those in [G.Y. Chen, X.X. Huang, Ekeland�s e-variational principle for set-valued mapping, Mathematical Methods of Operations Research 48 (1998) 181�186; G.Y. Chen, X.X. Huang, S.H. Hou, General Ekeland�s Variational Principle for Set-Valued Mappings, Journal of Optimization Theory and Applications 106 (2000) 151�164; S.J. Li, W.Y. Zhang, On Ekeland�s variational Principle for set-valued mappings, Acta Mathematicae Application Sinica, English Series 23 (2007) 141�148]. By the result, we prove some existence results for a general vector equilibrium problem under nonconvex and compact or noncompact assumptions of its domain, respectively. Moreover, we give some equivalent results to the variational principle.