Differential Calculus in Banach Spaces

1992 ◽  
pp. 35-53
Author(s):  
Philippe Blanchard ◽  
Erwin Brüning
Keyword(s):  
Banach Spaces ◽  
Differential Calculus

scholarly journals Restrictive metric regularity and generalized differential calculus in Banach spaces

2004 ◽  
Vol 2004 (50) ◽  
pp. 2653-2680 ◽  
Author(s):  
Boris S. Mordukhovich ◽  
Bingwu Wang
Keyword(s):  
Banach Spaces ◽  
Differential Calculus ◽  
Metric Regularity ◽  
Sufficient Conditions ◽  
Normal Cones ◽  
First Order ◽  
Nonconvex Sets ◽  
Generalized Differential ◽  
Necessary And Sufficient ◽  
Generalized Differential Calculus

We consider nonlinear mappingsf:X→Ybetween Banach spaces and study the notion ofrestrictive metric regularityoffaround some pointx¯, that is, metric regularity offfromXinto the metric spaceE=f(X). Some sufficient as well as necessary and sufficient conditions for restrictive metric regularity are obtained, which particularly include an extension of the classical Lyusternik-Graves theorem in the case whenfis strictly differentiable atx¯but its strict derivative∇f(x¯)is not surjective. We develop applications of the results obtained and some other techniques in variational analysis to generalized differential calculus involving normal cones to nonsmooth and nonconvex sets, coderivatives of set-valued mappings, as well as first-order and second-order subdifferentials of extended real-valued functions.

scholarly journals Different Concepts of Derivatives

2018 ◽  
Vol 3 ◽  
pp. 11
Author(s):  
Bhuwan Prasad Ojha
Keyword(s):  
Banach Spaces ◽  
Partial Derivative ◽  
Differential Calculus ◽  
Directional Derivative ◽  
Total Derivative ◽  
College Of Engineering

<p>In this paper, different concept of derivatives with some properties has been introduced. In differential calculus, the partial derivative, directional derivative and total derivative are studied. Their generalization for Banach spaces are the Gateaux differential and Freshet derivative.</p><p><strong>Journal of Advanced College of Engineering and Management,</strong> Vol.3, 2017, Page: 11-14</p>

DIFFERENTIAL CALCULUS ON BANACH SPACES

2000 ◽  
pp. 51-89
Author(s):  
YVONNE CHOQUET-BRUHAT ◽  
CÉCILE DEWITT-MORETTE
Keyword(s):  
Banach Spaces ◽  
Differential Calculus
Sign in / Sign up

Export Citation Format

Share Document