Fixed point theorems under weakly contractive conditions via auxiliary functions in ordered $G$-metric spaces

Abstract

We present some fixed point results for a single mapping and a pair of compatible mappings via auxiliary functions which satisfy a generalized weakly <span>contractive</span> condition in partially ordered complete <span>$G$</span>-metric spaces. Some examples are furnished to illustrate the <span>useability</span> 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.