| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 1708912 | Applied Mathematics Letters | 2012 | 4 Pages |
Abstract
Let us consider two nonempty subsets A,BA,B of a normed linear space XX, and let us denote by 2B2B the set of all subsets of BB. We introduce a new class of multivalued mappings {T:A→2B}{T:A→2B}, called R-KKM mappings, which extends the notion of KKM mappings. First, we discuss some sufficient conditions for which the set ∩{T(x):x∈A}∩{T(x):x∈A} is nonempty. Using this nonempty intersection theorem, we attempt to prove a extended version of the Fan–Browder multivalued fixed point theorem, in a normed linear space setting, by providing an existence of a best proximity point.
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Authors
V. Sankar Raj, S. Somasundaram,