Open Access

Generalized Vector Equilibrium-Like Problems without Pseudomonotonicity in Banach Spaces

Journal of Inequalities and Applications20072007:061794

DOI: 10.1155/2007/61794

Received: 10 January 2007

Accepted: 21 March 2007

Published: 8 May 2007


Let and be real Banach spaces, a nonempty closed convex subset of , and a multifunction such that for each is a proper, closed and convex cone with , where denotes the interior of . Given the mappings , , and , we study the generalized vector equilibrium-like problem: find such that for all for some . By using the KKM technique and the well-known Nadler result, we prove some existence theorems of solutions for this class of generalized vector equilibrium-like problems. Furthermore, these existence theorems can be applied to derive some existence results of solutions for the generalized vector variational-like inequalities. It is worth pointing out that there are no assumptions of pseudomonotonicity in our existence results.


Authors’ Affiliations

Department of Mathematics, Shanghai Normal University
Department of Business Administration, College of Management, Yuan-Ze University
Department of Applied Mathematics, National Sun Yat-Sen University


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© Lu-Chuan Ceng et al. 2007

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