We present some fixed point results for a single mapping and a pair of compatible mappings via auxiliary functions which satisfy a generalized weakly contractive condition in partially ordered complete G–metric spaces. Some examples are furnished to illustrate the useability of our main results. At the end, an application is presented to the study of existence and uniqueness of solutions for a boundary value problem for certain second order ODE and the respective integral equation. © 2018, Semnan University, Center of Excellence in Nonlinear Analysis and Applications. All rights reserved.