A sufficient condition for the existence and uniqueness of fixed point for a new variant of cyclic contractive mapping, named as weakly cyclic contractive mappings, involving a generalized altering distance function in complete metric spaces are provided. Examples are given to support the usability of our results. At the end of the results, an application to the study of existence and uniqueness of solutions for a class of two-point boundary value problem of second order differential equation is discussed by using the fixed point results. © 2014.