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  • Research Article
  • Open Access

Generalized Vector Equilibrium-Like Problems without Pseudomonotonicity in Banach Spaces

Journal of Inequalities and Applications20072007:061794

  • Received: 10 January 2007
  • Accepted: 21 March 2007
  • Published:


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.


  • Banach Space
  • Convex Subset
  • Existence Result
  • Existence Theorem
  • Generalize Vector


Authors’ Affiliations

Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China
Department of Business Administration, College of Management, Yuan-Ze University, Chung-Li City, Taoyuan Hsien, 330, Taiwan
Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, 804, Taiwan


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© Lu-Chuan Ceng et al. 2007

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