fréchet derivatives
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scholarly journals AN ALTERNATIVE APPROACH TO FRÉCHET DERIVATIVES

2020 ◽  
pp. 1-19
Author(s):  
SHANE ARORA ◽  
HAZEL BROWNE ◽  
DANIEL DANERS
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Banach Spaces ◽  
Short Proof ◽  
Banach Fixed Point Theorem ◽  
Alternative Approach ◽  
Frechet Derivatives ◽  
Fréchet Derivatives ◽  
The Schwarz Lemma

We discuss an alternative approach to Fréchet derivatives on Banach spaces inspired by a characterisation of derivatives due to Carathéodory. The approach allows many questions of differentiability to be reduced to questions of continuity. We demonstrate how that simplifies the theory of differentiation, including the rules of differentiation and the Schwarz lemma on the symmetry of second-order derivatives. We also provide a short proof of the differentiable dependence of fixed points in the Banach fixed point theorem.

Generalized Hukuhara Gâteaux and Fréchet derivatives of interval-valued functions and their application in optimization with interval-valued functions

2020 ◽  
Vol 510 ◽  
pp. 317-340 ◽  
Author(s):  
Debdas Ghosh ◽  
Ram Surat Chauhan ◽  
Radko Mesiar ◽  
Amit Kumar Debnath
Keyword(s):  
Frechet Derivatives ◽  
Fréchet Derivatives ◽  
Derivatives Of ◽  
Interval Valued

Time-migration velocity estimation using Fréchet derivatives based on nonlinear kinematic migration/demigration solvers

2020 ◽  
Vol 64 (1) ◽  
pp. 26-75
Author(s):  
Hao Zhao ◽  
Anders Ueland Waldeland ◽  
Dany Rueda Serrano ◽  
Martin Tygel ◽  
Einar Iversen
Keyword(s):  
Migration Velocity ◽  
Velocity Estimation ◽  
Time Migration ◽  
Frechet Derivatives ◽  
Fréchet Derivatives

scholarly journals On the second-order Fréchet derivatives of eigenvalues of Sturm–Liouville problems in potentials

2019 ◽  
Vol 113 (3) ◽  
pp. 301-312
Author(s):  
Shuyuan Guo ◽  
Guixin Xu ◽  
Meirong Zhang
Keyword(s):  
Second Order ◽  
Frechet Derivatives ◽  
Fréchet Derivatives ◽  
Sturm Liouville ◽  
Derivatives Of

scholarly journals Gâteaux and Fréchet derivatives of the operator of geometrically nonlinear bending problem of sandwich plate

2019 ◽  
Vol 1158 ◽  
pp. 022015
Author(s):  
I B Badriev ◽  
V Ju Bujanov ◽  
M V Makarov ◽  
N V Kalacheva
Keyword(s):  
Sandwich Plate ◽  
Geometrically Nonlinear ◽  
Nonlinear Bending ◽  
Frechet Derivatives ◽  
Fréchet Derivatives ◽  
Derivatives Of
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