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ArticleOriginal scientific text

Title

How to define "convex functions" on differentiable manifolds

Authors 1

Affiliations

  1. Institute of Mathematics of the Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, P.O. Box 21, Poland

Abstract

In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: 1. if M is a linear manifold, then (M) contains convex functions, 2. (·) is invariant under diffeomorphisms, 3. each f ∈ (M) is differentiable on a dense Gδ-set, is investigated.

Keywords

ENG
Fréchet differetiability, Gateaux differentiability, locally strongly paraconvex functions, C1,u-manifolds

Bibliography

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2009/29/1
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Pages:
7-17
Main language of publication
English
Received
2009-02-11
Published
2009

DOI: 10.7151/dmdico.1101

Exact and natural sciences