Total convexity for powers of the norm in uniformly convex banach spaces

Dan Butnariu; Alfredo N. Iusem; Elena Resmerita

Total convexity for powers of the norm in uniformly convex banach spaces

Dan Butnariu
, Alfredo N. Iusem
, Elena Resmerita

Department of Mathematics

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

Abstract

We show that in any uniformly convex Banach space the functions f(x) = ∥x∥^r with r ∈ (1, ∞) are totally convex. Using this fact we establish a formula for determining Bregman projections on closed hyperplanes and half spaces. This leads to a method for solving linear operator equations (e.g., first kind Fredholm and Volterra equations) in spaces which are uniformly convex and smooth.

Original language	English
Pages (from-to)	319-334
Number of pages	16
Journal	Journal of Convex Analysis
Volume	7
Issue number	2
State	Published - 2000

Keywords

Bregman projection
Duality mapping
Totally convex function
Uniformly convex Banach space

ASJC Scopus subject areas

Analysis
General Mathematics

Cite this

@article{3742281b3c3f45db9f4b22511beca463,

title = "Total convexity for powers of the norm in uniformly convex banach spaces",

abstract = "We show that in any uniformly convex Banach space the functions f(x) = ∥x∥r with r ∈ (1, ∞) are totally convex. Using this fact we establish a formula for determining Bregman projections on closed hyperplanes and half spaces. This leads to a method for solving linear operator equations (e.g., first kind Fredholm and Volterra equations) in spaces which are uniformly convex and smooth.",

keywords = "Bregman projection, Duality mapping, Totally convex function, Uniformly convex Banach space",

author = "Dan Butnariu and Iusem, \{Alfredo N.\} and Elena Resmerita",

year = "2000",

language = "English",

volume = "7",

pages = "319--334",

journal = "Journal of Convex Analysis",

issn = "0944-6532",

publisher = "Heldermann Verlag",

number = "2",

}

TY - JOUR

T1 - Total convexity for powers of the norm in uniformly convex banach spaces

AU - Butnariu, Dan

AU - Iusem, Alfredo N.

AU - Resmerita, Elena

PY - 2000

Y1 - 2000

N2 - We show that in any uniformly convex Banach space the functions f(x) = ∥x∥r with r ∈ (1, ∞) are totally convex. Using this fact we establish a formula for determining Bregman projections on closed hyperplanes and half spaces. This leads to a method for solving linear operator equations (e.g., first kind Fredholm and Volterra equations) in spaces which are uniformly convex and smooth.

AB - We show that in any uniformly convex Banach space the functions f(x) = ∥x∥r with r ∈ (1, ∞) are totally convex. Using this fact we establish a formula for determining Bregman projections on closed hyperplanes and half spaces. This leads to a method for solving linear operator equations (e.g., first kind Fredholm and Volterra equations) in spaces which are uniformly convex and smooth.

KW - Bregman projection

KW - Duality mapping

KW - Totally convex function

KW - Uniformly convex Banach space

UR - https://www.scopus.com/pages/publications/25644452862

M3 - Article

AN - SCOPUS:25644452862

SN - 0944-6532

VL - 7

SP - 319

EP - 334

JO - Journal of Convex Analysis

JF - Journal of Convex Analysis

IS - 2

ER -

Total convexity for powers of the norm in uniformly convex banach spaces

Abstract

Keywords

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this