On Multivalued Cosine Families

نویسنده

  • M. PISZCZEK
چکیده

Let K be a convex cone in a real Banach space. The main purpose of this paper is to show that for a regular cosine family {Ft : t ∈ R} of linear continuous multifunctions Ft : K → cc(X) there exists a linear continuous multifunction H : K → cc(K) such that Ft(x) ⊂ ∞ X n=0 t (2n)! H(x). Let X be a real normed vector space. We will denote by n(X) the family of all nonempty subsets of X and by cc(X) the family of all nonempty compact and convex subsets of X. For A,B ⊂ X and t ∈ R we introduce A+B = {a+ b : a ∈ A, b ∈ B}, tA = {ta : a ∈ A}. A subset K of X is called a cone if tK ⊂ K for all t ∈ (0,+∞). A cone is said to be convex if it is a convex set. Let A, B, C be sets of cc(X). We say that the set C is the Hukuhara difference of A and B, i.e., C = A − B if B + C = A. By the R̊adström Lemma [12] it follows that if this difference exists, then it is unique. 2000 Mathematics Subject Classification. Primary: 26E25, 28B20, 47D09.

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تاریخ انتشار 2007