KKM-type theorems for best proximity points
نویسندگان
چکیده
Let us consider two nonempty subsets A, B of a normed linear space X , and let us denote by 2B the set of all subsets of B. We introduce a new class of multivalued mappings {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} 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. © 2011 Elsevier Ltd. All rights reserved.
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ورودعنوان ژورنال:
- Appl. Math. Lett.
دوره 25 شماره
صفحات -
تاریخ انتشار 2012