Hermite-Hadamard inequality in the geometry of banach spaces

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Kikianty, Eder (2010) Hermite-Hadamard inequality in the geometry of banach spaces. PhD thesis, Victoria University.

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)
URI https://vuir.vu.edu.au/id/eprint/15793
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Historical > Faculty/School/Research Centre/Department > School of Engineering and Science
Historical > FOR Classification > 0103 Numerical and Computational Mathematics
Keywords Banach space theory, theory of means, theory of inequalities, Hermite-Hadamard inequality, Ostrowski inequality, Gruss inequality, inner product spaces, orthogonality
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