fréchet subdifferentials
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2020 ◽  
Vol 36 (1) ◽  
pp. 15-26
Author(s):  
TRUONG QUANG ALI

In this paper, we study Fréchet vector subdifferentials of vector-valued functions in normed spaces which reduceto the known ones of extended-real-valued functions. We establish relations between two kinds of Fréchet vectorsubdifferentials and between subdifferential and coderivative; some of them improve the existing relations forextended-real-valued functions. Finally, sum and chain rules among others for Fréchet subdifferentials of vector-valued functions are formulated and verified. Many examples are provided



2013 ◽  
Vol 21 (4) ◽  
pp. 661-671 ◽  
Author(s):  
Marián Fabian ◽  
Alexander Ioffe




2010 ◽  
Vol 43 (3) ◽  
Author(s):  
Jean-Paul Penot

AbstractWe present a simple proof of the separable reduction theorem, a crucial result of nonsmooth analysis which allows to extend to Asplund spaces the results known for separable spaces dealing with Fréchet subdifferentials. It relies on elementary results in convex analysis and avoids certain technicalities.







2000 ◽  
Vol 13 (1) ◽  
pp. 51-72 ◽  
Author(s):  
Tiziana Cardinali

In this paper we consider a Cauchy problem in which is present an evolution inclusion driven by the Fréchet subdifferential o ∂−f of a function f:Ω→R∪{+∞} (Ω is an open subset of a real separable Hilbert space) having a φ-monotone . subdifferential of order two and a perturbation F:I×Ω→Pfc(H) with nonempty, closed and convex values.First we show that the Cauchy problem has a nonempty solution set which is an Rδ-set in C(I,H), in particular, compact and acyclic. Moreover, we obtain a Kneser-type theorem. In addition, we establish a continuity result about the solution-multifunction x→S(x). We also produce a continuous selector for the multifunction x→S(x). As an application of this result, we obtain the existence of solutions for a periodic problem.



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