Fixed point results for generalized contractions in gauge spaces and applications

Abstract

In this paper, we present fixed point results for generalized contractions defined on a complete gauge space E. Also, we consider families of generalized contractions {ft : X → E}t∈[0,1] where X ⊂ E is closed and can have empty interior. We give conditions under which the existence of a fixed point for some ft0 imply the existence of a fixed point for every ft. Finally, we apply those results to infinite systems of first order nonlinear differential equations and to integral equations on the real line.