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Guidelines_English_Final
تحميل الدليل التدريبي

أسئلة شائعة


 

 

 

 

Applied Functional Analysis

 

Syllabus

Convex sets, Hahn-Banach separation,  convex functions,  conjugate

of a function, Sub-differential, Optimization problems, Hilbert spaces, Banach

 spaces, non-expansive  mappings, iterative methods for fixed points

 

 

 

   Time         :               Wednesday. 8: 30 – 11:30

  Credit hours:              3h

 Required textbook :     

1. Convex Analysis  by R. Tyrrell Rockafellar

2. Introductory Functional Analysis with Applications by Erwin Kreyszig

 

Course Details

Chap 1. Convex sets    

  1. Definition and examples
  2. Properties of convex sets
  3. Topological Properties of convex sets
  4. Hahn-Banach separation theorems
  5. Some applications

Chap 2.  Convex functions (2 weeks)

  1. Definitions and examples
  2. Continuity of convex functions
  3. Differentiability of convex functions

Chap 3.  Conjugate and subdifferential of convex functions

  1. Definitions and examples
  2. Lower and upper hemi-continuity of a function
  3. Conjugate of a function
  4. Subdifferential of  a function
  5. Some applications

Chap 4. Hilbert Spaces

  1. Inner product spaces. Hilbert spaces
  2. Properties of Hilbert spaces
  3. Representation of a functional   on Hilbert spaces
  4. Hilbert-Adjoint operator
  5. Self-Adjoint, unitary  and normal operators

 

Chap 5. Basic concepts in Banach spaces

  1. Definition and Properties of Banach spaces
  2. Uniform Boundedness Theorem 
  3. Strong and Weak convergence
  4. Open Mapping Theorem

 

 Chap 6. Iterative methods for fixed points 

  1. The Modulus of smoothness 
  2. Uniformly smooth Banach  spaces 
  3. Nonexpansives mappings
  4. Hapern, Lions and Reich algorithms

 

 

 

 

 

 

 

 

 

 

 
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