V-Proximal Trustworthy Banach Spaces
Open Access
- 5 June 2020
- journal article
- research article
- Published by Hindawi Limited in Journal of Function Spaces
- Vol. 2020, 1-5
- https://doi.org/10.1155/2020/4274160
Abstract
In a recent work (2016), 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<infinity as well as the sequence spaces l(p)(1 < p<infinity), the Sobolev spaces W-p,W-n (1 < p<infinity), and the Schatten trace ideals C-p(1 < p<infinity).Funding Information
- Deanship of Scientific Research, King Saud University (RGP-024)
This publication has 9 references indexed in Scilit:
- Calculus Rules for-Proximal Subdifferentials in Smooth Banach SpacesJournal of Function Spaces, 2016
- Regularity Concepts in Nonsmooth AnalysisSpringer Optimization and Its Applications, 2012
- Proximal analysis in reflexive smooth Banach spacesNonlinear Analysis, 2010
- Renormings of L p (L q )Mathematical Proceedings of the Cambridge Philosophical Society, 1999
- Nonsmooth sequential analysis in Asplund spacesTransactions of the American Mathematical Society, 1996
- Mean value property and subdifferential criteria for lower semicontinuous functionsTransactions of the American Mathematical Society, 1995
- Sharp uniform convexity and smoothness inequalities for trace normsInventiones Mathematicae, 1994
- Proximal Analysis and Approximate SubdifferentialsJournal of the London Mathematical Society, 1990
- ON SUBDIFFERENTIABILITY SPACESAnnals of the New York Academy of Sciences, 1983