BOUCHAIB FERRAHI ÝÑÇÍí ÈæÔÚíÈ ãÑÍÈÇ Welcome Bienvenue

 PhD in Mathematical sciences

Doctorat en Sciences Mathématiques

Qualification Française N° 05226158879 (25/02/2005)

• Formation and Research Unit: Numerical Analysis and Optimisation
• Research Team: Convex Analysis, Probability and Applications.
• E-mail: ferrahi@yahoo.com
• Phone : +212 67 04 26 67
• Fax: +212 37 77 54 71
• Address: Université Mohammed V - Agdal, Faculté des Sciences, Département de Mathématiques et d'Informatique, Av. Ibn Battouta, B.P 1014 Rabat 10000 Morocco

     Curriculum Vitae :   Français    English  CV.doc 

     List of Publications

      Thesis  Thèse  Thèse.pdf

     Research Activities:

            Regularity of Variational Integrals

            Geometry of Banach and Integral Spaces

        

    We study  regularity (lower semicontinuity, inf-compactness,...) of integrals (called also variational functionals or integral functionals) of the form $I_f(u,v)=\int\limits_\Omega f(\omega,u(\omega),v(\omega))d\mu$. Here X and Y  are Banach spaces and f is a real-valued function chosen from a class of functions called "integrands" with domain $\Omega\times X\times Y$. Such variational integrals are of considerable interest in the Calculus of Variations as well as in the field of Optimal Control. In the past, most of the work done on such integrals assumed that X  and Y are finite dimensional, and the tools used often required that assumption. Our purpose is to deal with the natural situation where the Banach spaces are infinite dimensional.

    The inf-compactness of these variational integrals is also studied. We say that an extended real-valued function f on a topological space E is inf-compact if for all real numbers c, the set {f<= c} is compact in E. Young functions $\psi$  and Orlicz spaces $L_\psi$ are introduced into the theory. The results are stated in terms of compactness conditions in the weak topology on Orlicz space $L_\psi$.

  Papers:

Abstract   .pdf    .ps    .dvi 

2. B. Ferrahi, A. Bourass et N.Saidou, Functional Measures and Inf-compactness of Integral Functionals. In “Inequality Theory and Applications”, Nova Science Publishers, Inc., New York. Vol. 4  (à paraître).   

Abstract .pdf  .ps   .dvi

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    We study of the geometry of Banach and Integral spaces. On one hand, We studied relations between the differentiability and some geometrical properties (e.g., extremality, dentability,...) of convex functions defined on a Banach space. On the other hand, we studied extremality and dentability in Orlicz spaces $L_\psi$.

  Papers:

1.  B. Ferrahi, A. Bourass and  N.Saidou, Extremality and differentiability of   convex  functions. Bulletin of  Polish  Academy of Sciences, Vol. 51, No1 (2003) 13 - 29.  

Abstract  .pdf  .ps  .dvi

2.  B. Ferrahi,A. Bourass and N. Saidou, A New Characterization of the Radon-Nikodym Property. in "Differential Equations and Applications, Vol. 3", Nova Science Publishers, Inc., New York (2004) 53 - 56.    

Abstract  .pdf  .ps  .dvi

3.  B. Ferrahi, Extremality and Convergence in Orlicz Spaces. in "Fixed Point Theory and Application”, Nova Science Publishers, Inc., New York. Vol 5 (2003) 23 - 32.

Abstract  .pdf  .ps  .dvi

    In this topic we study multivalued linear and random multivalued linear operators. The purpose is to develop the functional analysis of multivalued linear maps and random multivalued linear maps. The classical tools of functional analysis are extended to multivalued linear mappings between general topological vector spaces. We develop also Random versions of these classical tools.

Papers:

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