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

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

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.