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On generalized implicit vector equilibrium problems in Banach spaces

✍ Scribed by Lu-Chuan Ceng; Sy-Ming Guu; Jen-Chih Yao

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 550 KB
Volume: 57
Category: Article
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2009.02.026

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✦ Synopsis

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

introduce and consider the generalized implicit vector equilibrium problem: Find

)) ∈ -intC(u * ). By using the KKM technique and the well-known Nadler's result, we prove some existence theorems of solutions for this class of generalized implicit vector equilibrium problems. Our theorems extend and improve the corresponding results of several authors.

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