New fixed point theorems andcharacterization of the continuity inColombeau algebra

Abstract

In the present article, we investigate a new concept of fixedpoint theorems in the framework of Colombeau algebra of gen-eralized funtions. introduce a characterisation of the continuity of some C−linear maps, We gave another representation of the contraction of the maps among Colombian algebras.In addition, wehave given a general frame of fixed-point theorems in the clas-sic: the fixed point theorems of Banach, Kannan and Chatterjea.We concluded the applicability of these results by an application.