Academic Journal
On quadratic set valued functions
| Title: | On quadratic set valued functions |
|---|---|
| Authors: | Nikodem, Kazimierz |
| Source: | Publicationes Mathematicae Debrecen. 30:297-301 |
| Publisher Information: | University of Debrecen/ Debreceni Egyetem, 2022. |
| Publication Year: | 2022 |
| Subject Terms: | Functional equations for functions with more general domains and/or ranges, quadratic functionals, 0101 mathematics, set valued functions, 01 natural sciences, Functional equations and inequalities |
| Description: | A set valued function \(U:{\mathbb{R}}\to 2^ X\) (where X is a real normed space) is said to be quadratic iff \(U(s+t)+U(s-t)=2U(s)+2U(t),\) for all s,\(t\in {\mathbb{R}}\). There is proved, among others, that if a quadratic set valued function U:\({\mathbb{R}}\to CC(X)\) (where CC(X) denotes the family of all compact, convex and non-empty subsets of X) is bounded on a subset of \({\mathbb{R}}\) of positive inner Lebesgue measure or if it is measurable, then it is of the form \(U(t)=t^ 2U(1),\) \(t\in {\mathbb{R}}\). |
| Document Type: | Article |
| File Description: | application/xml |
| ISSN: | 0033-3883 |
| DOI: | 10.5486/pmd.1983.30.3-4.11 |
| Access URL: | https://zbmath.org/3853649 |
| Accession Number: | edsair.doi.dedup.....94e87604c843355cbb5f968cb8fdda6f |
| Database: | OpenAIRE |
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