Quelques théorèmes du point fixe dans des espaces métriques et leurs applications

Abstract

The fixed point theory is a highly useful tool that is applied to almost all branches of mathematical analysis. by applying the other existing theories there are many problems that cannot be solved but can be easily resolved by using this theory. In this work, we explore several fixed-point theorems, for various appli- cations, defined on complete metric spaces with special conditions, such as the Banach theorem, Kannan theorem, Chatterjea theorem, Suzuki theo- rem, theorem of Berinde, and others. Throughout this study, we detailed some proofs and give several examples for some of these theorems. Finally, we apply some of these theorems to study the existence pro- blem of solutions for systems of linear equations and ordinary differential equations