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

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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.",

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AU - Iusem, Alfredo N.

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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.

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KW - Duality mapping

KW - Totally convex function

KW - Uniformly convex Banach space

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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