Fixed point results for generalized contractions in gauge spaces and applications

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 {f(t) : X --> E}(t is an element of [0,1]) where X subset of E is closed and can have empty interior. We give conditions under which the existence of a fixed point for some f(t0) imply the existence of a fixed point for every f(t). Finally, we apply those results to infinite systems of first order nonlinear differential equations and to integral equations on the real line.