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.
Nashine,H K and Kumar Sharma,A . (2018). Fixed point theorems under weakly contractive conditions via auxiliary functions in ordered $G$-metric spaces. International Journal of Nonlinear Analysis and Applications, 9(2), 85-109. doi: 10.22075/ijnaa.2018.868.1157
MLA
Nashine,H K , and Kumar Sharma,A . "Fixed point theorems under weakly contractive conditions via auxiliary functions in ordered $G$-metric spaces", International Journal of Nonlinear Analysis and Applications, 9, 2, 2018, 85-109. doi: 10.22075/ijnaa.2018.868.1157
HARVARD
Nashine H K, Kumar Sharma A. (2018). 'Fixed point theorems under weakly contractive conditions via auxiliary functions in ordered $G$-metric spaces', International Journal of Nonlinear Analysis and Applications, 9(2), pp. 85-109. doi: 10.22075/ijnaa.2018.868.1157
CHICAGO
H K Nashine and A Kumar Sharma, "Fixed point theorems under weakly contractive conditions via auxiliary functions in ordered $G$-metric spaces," International Journal of Nonlinear Analysis and Applications, 9 2 (2018): 85-109, doi: 10.22075/ijnaa.2018.868.1157
VANCOUVER
Nashine H K, Kumar Sharma A. Fixed point theorems under weakly contractive conditions via auxiliary functions in ordered $G$-metric spaces. IJNAA. 2018;9(2):85-109. doi: 10.22075/ijnaa.2018.868.1157
International Journal of Nonlinear Analysis and Applications