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Generalized Vector Equilibrium-Like Problems without Pseudomonotonicity in Banach Spaces

Abstract

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.

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Correspondence to Lu-Chuan Ceng.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Ceng, LC., Guu, SM. & Yao, JC. Generalized Vector Equilibrium-Like Problems without Pseudomonotonicity in Banach Spaces. J Inequal Appl 2007, 061794 (2007). https://doi.org/10.1155/2007/61794

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Keywords

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