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Generalized vector complementarity-type problems in topological vector spaces

✍ Scribed by Suhel A. Khan

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
292 KB
Volume
59
Category
Article
ISSN
0898-1221

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✦ Synopsis

In this paper, we introduced the generalized vector variational inequality-type problem and the generalized vector complementarity-type problem in the setting of topological vector space. By utilizing a modified version of the Fan-KKM theorem, we investigated the nonemptyness and compactness of solution sets of these problems without the demipseudomonotonicity assumption. Further, we prove that solution sets of both the problems are equivalent to each other under some suitable conditions. The results of this paper generalize and improve several results that appeared recently in the literature.

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Let X and Y be real Banach spaces, K be a nonempty convex subset of X , and C : K β†’ 2 Y be a multifunction such that for each u ∈ K , C (u) is a proper, closed and convex cone with intC (u) = βˆ…, where intC (u) denotes the interior of C (u). Given the mappings introduce and consider the generalized