Opuscula Math. 32, no. 1 (2012), 159-170

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)

  • 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.
Opuscula Mathematica - cover

Cite this article as:
Ewelina Mainka-Niemczyk, Some properties of set-valued sine families, Opuscula Math. 32, no. 1 (2012), 159-170, http://dx.doi.org/10.7494/OpMath.2012.32.1.159

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.