New common best proximity point theorems in complete metric space with weak $P$-property

Document Type : Research Paper


1 Department of Mathematics, Quchan University of Technology, Quchan, Iran

2 Department of pure Mathematics, Shahrood University of Tehnology, Shahrood, Iran


In this paper, we define $\phi$-contraction, after that; we obtained the common best proximity point results for different types of contractions in the setting of complete metric spaces by using weak p-property and proved the uniqueness of these points. Also, we presented an example to support our results.