English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We present a random version of the Borwein-Preiss smooth variational principle, stating that under suitable conditions, the set of minimizers of a perturbed function depending on a random variable, admits a measurable selection. Two applications are given. The first one shows that if      E E       is a superreflexive Banach space, then any convex continuous integral functional on      L 1 ( T , μ  ; E ) L^1(T, \mu ; E)       from a certain class (in particular the usual      L 1 L^1       norm), is weak Hadamard differentiable on a subset whose complement is      σ  \sigma      -very porous. The second application is a random version of the Caristi fixed point theorem for multifunctions.

A random variational principle with application to weak Hadamard differentiability of convex integral functionals