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تحميل الدليل التدريبي

أسئلة شائعة





Applied Functional Analysis



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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