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Nashine, Hemant Kumar, Kumar Sharma, Atul. (1397). Fixed point theorems under weakly contractive conditions via auxiliary functions in ordered $G$-metric spaces. نشریه هنرهای کاربردی, 9(2), 85-109. doi: 10.22075/ijnaa.2018.868.1157
Hemant Kumar Nashine; Atul Kumar Sharma. "Fixed point theorems under weakly contractive conditions via auxiliary functions in ordered $G$-metric spaces". نشریه هنرهای کاربردی, 9, 2, 1397, 85-109. doi: 10.22075/ijnaa.2018.868.1157
Nashine, Hemant Kumar, Kumar Sharma, Atul. (1397). 'Fixed point theorems under weakly contractive conditions via auxiliary functions in ordered $G$-metric spaces', نشریه هنرهای کاربردی, 9(2), pp. 85-109. doi: 10.22075/ijnaa.2018.868.1157
Nashine, Hemant Kumar, Kumar Sharma, Atul. Fixed point theorems under weakly contractive conditions via auxiliary functions in ordered $G$-metric spaces. نشریه هنرهای کاربردی, 1397; 9(2): 85-109. doi: 10.22075/ijnaa.2018.868.1157

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

International Journal of Nonlinear Analysis and Applications
مقاله 8، دوره 9، شماره 2، اسفند 2018، صفحه 85-109    اصل مقاله (456.56 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2018.868.1157
نویسندگان
Hemant Kumar Nashine* 1؛ Atul Kumar Sharma2
1Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632014, TN, India
2Department of Mathematics, Lakhmi Chand Institute of Technology, Bilaspur-495001,(Chhattisgarh), India
تاریخ دریافت: 08 مرداد 1394،  تاریخ بازنگری: 08 آذر 1397،  تاریخ پذیرش: 17 آذر 1397 
چکیده
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.
کلیدواژه‌ها
$G$-metric space؛ Weakly contraction condition؛ Altering distance function؛ Compatible mappings؛ Coincidence point
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