Stability results for some classical convexity operations

Shiri Artstein-Avidan; Vitali Milman

doi:10.1515/advgeom-2012-0011

Stability results for some classical convexity operations

Shiri Artstein-Avidan, Vitali Milman

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We study stability and super-stability results, in isomorphic form, for several equations on transforms of convex functions and bodies. We show that additivity of mappings on convex functions is super-stable, and that for maps on closed convex sets which include 0 both additivity and order preservation are stable.

Original language	English
Pages (from-to)	51-70
Number of pages	20
Journal	Advances in Geometry
Volume	13
Issue number	1
DOIs	https://doi.org/10.1515/advgeom-2012-0011
State	Published - Jan 2013

All Science Journal Classification (ASJC) codes

Geometry and Topology

Access to Document

10.1515/advgeom-2012-0011

Cite this

@article{ce8727fa38e344a89ea961f4effc17bc,

title = "Stability results for some classical convexity operations",

abstract = "We study stability and super-stability results, in isomorphic form, for several equations on transforms of convex functions and bodies. We show that additivity of mappings on convex functions is super-stable, and that for maps on closed convex sets which include 0 both additivity and order preservation are stable.",

author = "Shiri Artstein-Avidan and Vitali Milman",

note = "Funding Information: ∗The first named author was partially supported by ISF grant 865/07. The second named author was partially supported by ISF grant 387/09. Both authors were partially supported by BSF grant 2006079.",

year = "2013",

month = jan,

doi = "10.1515/advgeom-2012-0011",

language = "الإنجليزيّة",

volume = "13",

pages = "51--70",

journal = "Advances in Geometry",

issn = "1615-715X",

publisher = "Walter de Gruyter GmbH",

number = "1",

}

TY - JOUR

T1 - Stability results for some classical convexity operations

AU - Artstein-Avidan, Shiri

AU - Milman, Vitali

N1 - Funding Information: ∗The first named author was partially supported by ISF grant 865/07. The second named author was partially supported by ISF grant 387/09. Both authors were partially supported by BSF grant 2006079.

PY - 2013/1

Y1 - 2013/1

N2 - We study stability and super-stability results, in isomorphic form, for several equations on transforms of convex functions and bodies. We show that additivity of mappings on convex functions is super-stable, and that for maps on closed convex sets which include 0 both additivity and order preservation are stable.

AB - We study stability and super-stability results, in isomorphic form, for several equations on transforms of convex functions and bodies. We show that additivity of mappings on convex functions is super-stable, and that for maps on closed convex sets which include 0 both additivity and order preservation are stable.

UR - http://www.scopus.com/inward/record.url?scp=84877961115&partnerID=8YFLogxK

U2 - 10.1515/advgeom-2012-0011

DO - 10.1515/advgeom-2012-0011

M3 - مقالة

SN - 1615-715X

VL - 13

SP - 51

EP - 70

JO - Advances in Geometry

JF - Advances in Geometry

IS - 1

ER -

Stability results for some classical convexity operations

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this