Fixed point theorems on orthogonal complete metric spaces with an application

Document Type : Research Paper

Authors

1 Equipe de Recherche en Math'{e}matiques Appliqu'{e}es, Technologies de l'Information et de la Communication Facult'{e} Polydisciplinare de Khouribga, Universit'{e} Sultan Moulay Slimane de Beni-Mellal, Morocco

2 Equipe de Recherche en Math'{e}matiques Appliqu'{e}es, Technologies de l'Information et de la Communication Facult'{e} Polydisciplinare de Khouribga, Universit'{e} Sultan Moulay Slimane de Beni-Mellal, Morocco

Abstract

In this paper, we introduce the concept of orthogonal contractive mappings and prove some fixed point theorems for such contractions. We establish our results in orthogonal bounded complete metric spaces via the notion of $\tau-$distances. Moreover, an application to a differential equation is given.

Keywords