Conjugate functions, L^{p}-norm like functionals, the generalized Hölder inequality, Minkowski inequality and subhomogeneity

Conjugate functions, L^{p}-norm like functionals, the generalized Hölder inequality, Minkowski inequality and subhomogeneity

For \(h:(0,\infty )\rightarrow \mathbb{R}\), the function \(h^{\ast }\left( t\right) :=th(\frac{1}{t})\) is called \((\ast)\)-conjugate to \(h\). This conjugacy is related to the Hölder and Minkowski inequalities. Several properties of \((\ast)\)-conjugacy are proved. If \(\varphi\) and \(\varphi ^{...

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Bibliographic Details
Main Author: Janusz Matkowski
Format: Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2014-01-01
Series:Opuscula Mathematica
Subjects:
\(L^{p}\)-norm like functional
homogeneity
subhomogeneity
subadditivity
the converses of Minkowski and Hölder inequalities
generalization of the Minkowski and Hölder inequalities
conjugate (complementary) functions
Young conjugate functions
convex function
geometrically convex function
Wright convex function
functional equation
Online Access:http://www.opuscula.agh.edu.pl/vol34/3/art/opuscula_math_3432.pdf

Internet

http://www.opuscula.agh.edu.pl/vol34/3/art/opuscula_math_3432.pdf

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