### Abstract

We give a geometric characterization of the convex subsets of a Banach space with the property that for any two convex continuous functions on this set, if their sum is Lipschitz, then the functions must be Lipschitz. We apply this result to the theory of Δ-convex functions.

Original language | English (US) |
---|---|

Pages (from-to) | 269-286 |

Number of pages | 18 |

Journal | Studia Mathematica |

Volume | 158 |

Issue number | 3 |

State | Published - 2003 |

### Fingerprint

### Keywords

- Δ-convex mappings
- Convex functions
- Lipschitz functions

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Studia Mathematica*,

*158*(3), 269-286.

**Lipschitz sums of convex functions.** / Csörnyei, Marianna; Naor, Assaf.

Research output: Contribution to journal › Article

*Studia Mathematica*, vol. 158, no. 3, pp. 269-286.

}

TY - JOUR

T1 - Lipschitz sums of convex functions

AU - Csörnyei, Marianna

AU - Naor, Assaf

PY - 2003

Y1 - 2003

N2 - We give a geometric characterization of the convex subsets of a Banach space with the property that for any two convex continuous functions on this set, if their sum is Lipschitz, then the functions must be Lipschitz. We apply this result to the theory of Δ-convex functions.

AB - We give a geometric characterization of the convex subsets of a Banach space with the property that for any two convex continuous functions on this set, if their sum is Lipschitz, then the functions must be Lipschitz. We apply this result to the theory of Δ-convex functions.

KW - Δ-convex mappings

KW - Convex functions

KW - Lipschitz functions

UR - http://www.scopus.com/inward/record.url?scp=0142199428&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0142199428&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0142199428

VL - 158

SP - 269

EP - 286

JO - Studia Mathematica

JF - Studia Mathematica

SN - 0039-3223

IS - 3

ER -