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Smooth negligibility and subdifferential calculus in
 

Summary: Smooth negligibility and
subdifferential calculus in
Banach spaces, with
applications
Daniel Azagra
Doctoral dissertation directed by Jes´us A. Jaramillo
DEPARTAMENTO DE AN´ALISIS MATEM´ATICO
FACULTAD DE CIENCIAS MATEM´ATICAS
UNIVERSIDAD COMPLUTENSE DE MADRID
October, 1997
Contents
Introduction 2
1 Spheres and hyperplanes 13
2 Rolle's theorem 23
2.1 Failure of Rolle's theorem in infinite dimensions . . . . . . . . . . . . 23
2.2 An approximate Rolle's theorem . . . . . . . . . . . . . . . . . . . . 25
3 Some subdifferential calculus 32
3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Subdifferential Mean Value Inequality Theorem . . . . . . . . . . . . 44
3.3 Subdifferential Approximate Rolle's Theorem . . . . . . . . . . . . . 47

  

Source: Azagra Rueda, Daniel - Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid

 

Collections: Mathematics