\(V\)-proximal trustworthy Banach spaces
type: Item
instance of: scholarly article
title: \(V\)-proximal trustworthy Banach spaces
zbMATH Open document ID: 1457.46073
DOI: 10.1155/2020/4274160
author: Messaoud Bounkhel
author: Mostafa Bachar
published in: Journal of Function Spaces
publication date: 2020-07-15T00:00:00Z
review text: Summary: In [ibid. 2016, Article ID 1917387, 12 p. (2016; Zbl 1348.49012)], the first author proved the fuzzy sum rule for the \(V\)-proximal subdifferential under some natural assumptions on an equivalent norm of the Banach spaces. In the present paper, we are going to prove that the class of Banach spaces satisfying the fuzzy sum rule is very large and contains all \(L^p\) spaces \(1<p<\infty\) as well as the sequence spaces \(l^p$ $\left( 1 < p < \infty\right)\), the Sobolev spaces \(W^{p,n}$ $(1<p<\infty)\), and the Schatten trace ideals \(\mathbf{C}^p $ $(1<p<\infty)\).
Mathematics Subject Classification ID: 46S40
Mathematics Subject Classification ID: 46G05
zbMATH DE Number: 7220560
zbMATH Keywords: fuzzy sum rule
zbMATH Keywords: \(V\)-proximal subdifferential
zbMATH Keywords: \(V\)-proximal trustworthy Banach space
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/4274160
OpenAlex ID: W3033791272
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description: scientific article; zbMATH DE number 7220560