Chapter Thirteen: Fréchet differentiability of vector-valued functionsLindenstraussJoram / PreissDavid / TierJaroslav
Our results are generalizations of Rolewicz's theorems (Theorem3.1) from Rolewicz [Differentiability of strongly paraconvex vector-valued functions. Funct Approx. 2011;2:273–277].doi:10.1080/02331934.2019.1653296E. M. BednarczukK. W. Leniewski...
open set U having the point X:(x1,x2,...,xn) and the point ||H|| such that the point X + H lies in the set we try to define the meaning of the derivative. \frac{f(X \ + \ H) \ - \ f(X)}{H} is an undefined quantity, what does it mean to divide by a vector.....
Applications of these results are given to the space "(E) of all bounded sequences in E and to the space B("1,E) of all bounded linear operators from "1 into E关键词: Banach space continuos functions vector-valued functions supremum norm smooth points ...
(Sub-)Differentiability of Probability Functions with Elliptical Distributions In this paper we investigate probability functions acting on nonlinear systems wherein the random vector can follow an elliptically symmetric distribution... W Van Ackooij,I Aleksovska,M Munoz-Zuniga - Set-valued and variatio...
For an arbitrary infinite-dimensional Banach space , we construct examples of strongly-measurable -valued Pettis integrable functions whose indefinite Pettis integrals are nowhere weakly differentiable; thus, for these functions the Lebesgue Differentiation Theorem fails rather spectacularly. We also relate ...
Almgren, Jr. F.J.: Almgren’s Big Regularity Paper, Volume 1 of World Scientific Monograph Series in Mathematics. World Scientific Publishing Co. Inc., River Edge (2000).\(Q\)-valued functions minimizing Dirichlet’s integral and the regularity of area-minimizing rectifiable currents up to cod...
Even though such techniques result to more complex objective functions, metaheuristic search methods are well equipped to handle them efficiently. Finally, it must be noted that the vast majority of optimization methodologies can inherently handle only unconstrained problems. It is a fact that the OPF...
is the class of the admissible functions, with u0∈W1,p(Ω) a fixed boundary datum. Let us observe that u∈Wloc1,p(Ω) is a solution to obstacle problem (1.1) in 𝒦ψ(Ω) if and only if u∈𝒦ψ(Ω) and u is a solution to the variational inequality (1.2)∫...
In this paper, a problem is discussed, that on a Banach space whether a vector valued function which is of strongly bounded variation isstrongly differentiablealmost everywhere or not. 本文讨论Banach空间上强有界变差的向量值函数 ,是否一定几乎处处强可导 。