Abstract and Applied Analysis

$\sigma$-Porosity in monotonic analysis with applications to optimization

A. M. Rubinov

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We introduce and study some metric spaces of increasing positively homogeneous (IPH) functions, decreasing functions, and conormal (upward) sets. We prove that the complements of the subset of strictly increasing IPH functions, of the subset of strictly decreasing functions, and of the subset of strictly conormal sets are σ-porous in corresponding spaces. Some applications to optimization are given.

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Abstr. Appl. Anal., Volume 2005, Number 3 (2005), 287-305.

First available in Project Euclid: 25 July 2005

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Rubinov, A. M. $\sigma$-Porosity in monotonic analysis with applications to optimization. Abstr. Appl. Anal. 2005 (2005), no. 3, 287--305. doi:10.1155/AAA.2005.287. https://projecteuclid.org/euclid.aaa/1122298430

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