Abdalla Tallafha, Tariq Qaeasmeh, Nedal Tahat, Wasfi Shatanawi, Anwar Bataihah, and Kamal Abodayeh. Some Coincidence Point and Some Fixed-Point Results in Ordered Metric Spaces and Application. Dynamic Systems and Applications 30 (2021) No.1, 143-156

https://doi.org/10.46719/dsa202130110

ABSTRACT.
Introducing some new nonlinear contractions in the setting of metric spaces is one of the most important method to establish new common fixed point results under a certain of conditions. In this manuscript, a new coincidence point result for compatible mappings in ordered metric spaces are proved by introducing new contraction based on two comparable elements. Also, we utilize our result to prove and derive some new fixed point theorems. In addition, we introduce an example an application to support our results.

 AMS (MOS) Subject Classification. 46T99.

Key Words: Ordered metric space; coincidence point; fixed point theorems; compatible mappings; nonlinear contraction.