## Taiwanese Journal of Mathematics

### LINEAR REGULARITY FOR AN INFINITE SYSTEM FORMED BY $\small\textit{p}$-UNIFORMLY SUBSMOOTH SETS IN BANACH SPACES

Zhou Wei

#### Abstract

In this paper, we introduce and study $p$-uniform subsmoothness of a collection of infinitely many closed sets in a Banach space. Using variational analysis and techniques, we mainly study linear regularity for a collection of infinitely many closed sets satisfying $p$-uniform subsmoothness. The necessary or/and sufficient conditions on the linear regularity are obtained in this case. In particular, we extend the characterizations of linear regularity for a collection of infinitely many closed convex sets to the nonconvex setting.

#### Article information

Source
Taiwanese J. Math., Volume 16, Number 1 (2012), 335-352.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406544

Digital Object Identifier
doi:10.11650/twjm/1500406544

Mathematical Reviews number (MathSciNet)
MR2887868

Zentralblatt MATH identifier
1235.90155

#### Citation

Wei, Zhou. LINEAR REGULARITY FOR AN INFINITE SYSTEM FORMED BY $\small\textit{p}$-UNIFORMLY SUBSMOOTH SETS IN BANACH SPACES. Taiwanese J. Math. 16 (2012), no. 1, 335--352. doi:10.11650/twjm/1500406544. https://projecteuclid.org/euclid.twjm/1500406544

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