  In this paper we introduce and study new classes of mappings in metric
spaces. The main class of mappings is called generalized orbital triangular
contractions and it generalizes some existing results (such as Banach
contractions, mappings contracting perimeters of triangles). We prove that
these contractions are not necessarily continuous and have a unique fixed point
under certain conditions. Moreover, we extend our class to generalized orbital
triangular Kannan contractions and generalized orbital triangular Chatterjea
contractions.
