Hermite-Hadamard inequality in the geometry of banach spaces
Tools
Tools
Kikianty, Eder (2010) Hermite-Hadamard inequality in the geometry of banach spaces. PhD thesis thesis, Victoria University.
![[img]](http://vuir.vu.edu.au/style/images/fileicons/application_pdf.png) | PDF Download (1017kB) |
Abstract
The theory of inequalities has made significant contributions in many areas of mathematics. The purpose of this dissertation is to employ inequalities in studying the geometry of a Banach space. Motivated by the Hermite-Hadamard inequality, a new family of norms is defined, which is called the p-HH-norm. The research outcomes of this thesis make significant contributions in Banach space theory, the theory of means and the theory of inequalities. These contributions including the characterization of inner product spaces via orthogonality; the extension of means of positive numbers to a vector space setting; and the developments of some important inequalities, namely the Hermite-Hadamard inequality, Ostrowski inequality and Gruss inequality in linear spaces.
| Item Type: | Thesis (PhD thesis) |
|---|---|
| Uncontrolled Keywords: | Banach space theory, theory of means, theory of inequalities, Hermite-Hadamard inequality, Ostrowski inequality, Gruss inequality, inner product spaces, orthogonality |
| Subjects: | FOR Classification > 0101 Pure Mathematics Faculty/School/Research Centre/Department > School of Engineering and Science FOR Classification > 0103 Numerical and Computational Mathematics |
| Depositing User: | VU Library |
| Date Deposited: | 24 Aug 2010 00:24 |
| Last Modified: | 21 May 2013 05:31 |
| URI: | http://vuir.vu.edu.au/id/eprint/15793 |
| ePrint Statistics: | View download statistics for this item |
| Repository staff only |
Reporting copyright infringements & problems
The Victoria University is committed to upholding the rights of copyright owners. If you believe that copyright material is available on the Victoria University network in such a way that it constitutes a copyright infringement or a breach of a contract or licence, please contact us.
