Opuscula Math. 32, no. 1 (2012), 159-170
http://dx.doi.org/10.7494/OpMath.2012.32.1.159
Opuscula Mathematica
Some properties of set-valued sine families
Abstract. Let \(\{F_t : t \geq 0\}\) be a family of continuous additive set-valued functions defined on a convex cone \(K\) in a normed linear space \(X\) with nonempty convex compact values in \(X\). It is shown that (under some assumptions) a regular sine family associated with \(\{F_t : t \geq 0\}\) is continuous and \(\{F_t : t \geq 0\}\) is a continuous cosine family.
Keywords: set-valued sine and cosine families, continuity of sine families, Hukuhara differences, concave set-valued functions.
Mathematics Subject Classification: 26E25, 47H04, 47D09, 39B52.
- Ewelina Mainka-Niemczyk
- Silesian University of Technology, Institute of Mathematics, Kaszubska 23, 44-100 Gliwice, Poland
- Received: 2010-11-02.
- Revised: 2011-02-02.
- Accepted: 2011-03-05.
