Best `omega`-Proximity Point For `omega`-Proximal Quasi Contraction Mappings in Modular Metric Spaces

In this paper we introduce `omega`-proximal quasi contraction mapping and best `omega`-proximity point in modular metric spaces. In fact, we show that every `omega`-proximal quasi contraction mapping has unique best `omega`-proximity point in modular metric spaces. Finally, we give an example to illustrate the applications of our results.

Keywords:

modular metric space , best proximity point , proximal quasi contraction map , $omega$-proximal quasi contraction , proximal Picard sequence and T-orbitally $omega$-complete.