Abdelhakim Maaden,
Abdelkader Stouti
Address.
Unit\'e de Recherche
Math\'ematiques et Applications, Facult\'e des Sciences
et Techniques, B.P.
523, Beni
- Mellal, Maroc
E-mail:
hmaaden2002@yahoo.fr
Abstract.
It is shown that under
natural assumptions, there exists a linear functional does not have supremum
on a closed bounded subset. That is
the James Theorem for non-convex bodies. Also, a non-linear
version of the Bishop-Phelps
Theorem and a geometrical version of the formula
of the subdifferential
of the sum of two functions
are obtained.
AMSclassification. 46B20.
Keywords. James Theorem, Bishop-Phelps Theorem, smooth variational principles.