Quelques aspects de la théorie du point fixe pour les semi-groupes

Abstract

This work concerns several aspects of the theory of fixed points for some left reversible semigroups. It is divided into three parts, which are corresponding to the type of semigroup. In the first part, we study the fixed point problem for a Lipschitzian semigroup in a Hilbert space, then in a metric space with uniform normal structure. In the Hilbert space case, we study the relationship between the Lipschitz mappings constants of semigroup and Lifschitz character of Hilbert space. In the second case we give and uniform normal structure coefficient. In the second part, we introduce the notion of near-contractive mappins then we show that any semigroup generated by near-contractive selfmap on a complete metric space has a unique fixed point in this space, furthermore the Picard iterates converge to the fixed point. In the third part, we used the notion of φ–contractive semigroup in general probabilistic metric spaces for to establish some fixed point theorems for this type of semigroup.