A Convexity Inequality

2002 ◽  
Vol 109 (1) ◽  
pp. 64 ◽  
Author(s):  
Paolo Roselli ◽  
Michel Willem
Keyword(s):  
Convexity Inequality

scholarly journals A maximin characterisation of the escape rate of non-expansive mappings in metrically convex spaces

2011 ◽  
Vol 152 (2) ◽  
pp. 341-363 ◽  
Author(s):  
STÉPHANE GAUBERT ◽  
GUILLAUME VIGERAL
Keyword(s):  
Stochastic Games ◽  
Positive Curvature ◽  
Type Theorem ◽  
Escape Rate ◽  
Mild Form ◽  
Curvature Condition ◽  
Expansive Mapping ◽  
Zero Sum ◽  
Expansive Maps ◽  
Convexity Inequality

AbstractWe establish a maximin characterisation of the linear escape rate of the orbits of a non-expansive mapping on a complete (hemi-)metric space, under a mild form of Busemann's non-positive curvature condition (we require a distinguished family of geodesics with a common origin to satisfy a convexity inequality). This characterisation, which involves horofunctions, generalises the Collatz–Wielandt characterisation of the spectral radius of a non-negative matrix. It yields as corollaries a theorem of Kohlberg and Neyman (1981), concerning non-expansive maps in Banach spaces, a variant of a Denjoy–Wolff type theorem of Karlsson (2001), together with a refinement of a theorem of Gunawardena and Walsh (2003), concerning order-preserving positively homogeneous self-maps of symmetric cones. An application to zero-sum stochastic games is also given.

Nonexistence of Solutions of Some Non-Linear Non-Local Evolution Systems on the Heisenberg Group

2015 ◽  
Vol 18 (6) ◽  
Author(s):  
Mahmoud Boutefnouchet ◽  
Mokhtar Kirane
Keyword(s):  
Parabolic Equations ◽  
Hyperbolic Equations ◽  
Existence Results ◽  
Test Function ◽  
Nonexistence Of Solutions ◽  
Non Local ◽  
Linear Damping ◽  
Test Function Method ◽  
Convexity Inequality ◽  
Evolution Systems

AbstractWe present non-existence results for systems of non-local in space hyperbolic equations, for systems of non-local in space parabolic equations, and for systems of non-local in space hyperbolic equations with linear damping terms. Our method of proof is based on the test function method with a help of a convexity inequality recently proved in [2].

scholarly journals A noncommutative martingale convexity inequality

2016 ◽  
Vol 44 (2) ◽  
pp. 867-882 ◽  
Author(s):  
Éric Ricard ◽  
Quanhua Xu
Keyword(s):  
Noncommutative Martingale ◽  
Convexity Inequality

scholarly journals Convexity, boundedness, and almost periodicity for differential equations in Hillbert space

1979 ◽  
Vol 2 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Jerome A. Goldstein
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Bounded Solution ◽  
Normal Operator ◽  
Sufficient Condition ◽  
Differential Inequalities ◽  
Almost Periodic ◽  
Bounded Solutions ◽  
General Sufficient Condition ◽  
Convexity Inequality

There are three kinds of results. First we extend and sharpen a convexity inequality of Agmon and Nirenberg for certain differential inequalities in Hilbert space. Next we characterize the bounded solutions of a differential equation in Hilbert space involving and arbitrary unbounded normal operator. Finally, we give a general sufficient condition for a bounded solution of a differential equation in Hilbert space to be almost periodic.

A Convexity Inequality

2002 ◽  
Vol 109 (1) ◽  
pp. 64-70 ◽  
Author(s):  
Paolo Roselli ◽  
Michel Willem
Keyword(s):  
Convexity Inequality
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