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

Ewelina Mainka-Niemczyk

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.

Full text (pdf)