Article ID Journal Published Year Pages File Type
474072 Computers & Mathematics with Applications 2009 10 Pages PDF
Abstract

Let XX and YY be real Banach spaces, KK be a nonempty convex subset of XX, and C:K→2YC:K→2Y be a multifunction such that for each u∈Ku∈K, C(u)C(u) is a proper, closed and convex cone with intC(u)≠0̸, where intC(u) denotes the interior of C(u)C(u). Given the mappings T:K→2L(X,Y)T:K→2L(X,Y), A:L(X,Y)→L(X,Y)A:L(X,Y)→L(X,Y), f1:L(X,Y)×K×K→Yf1:L(X,Y)×K×K→Y, f2:K×K→Yf2:K×K→Y, and g:K→Kg:K→K, we introduce and consider the generalized implicit vector equilibrium problem: Find u∗∈Ku∗∈K such that for any v∈Kv∈K, there is s∗∈Tu∗s∗∈Tu∗ satisfying f1(As∗,v,g(u∗))+f2(v,g(u∗))∉−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.

Keywords
Related Topics
Physical Sciences and Engineering Computer Science Computer Science (General)
Authors
, , ,