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Generalized Vector Equilibrium-Like Problems without Pseudomonotonicity in Banach Spaces
Journal of Inequalities and Applications volume 2007, Article number: 061794 (2007)
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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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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DOI: https://doi.org/10.1155/2007/61794