Study of the generalized P-contractions on Banach spaces and uniqueness for stability fixed points

Document Type : Research Paper


1 Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Iraq.

2 Department of Physics, College of Education-Tuzkhurmatu , Tikrit University, Iraq.


This article aims to introduce some concepts such as $P$-contraction and  $G-P$-contraction which are defined on Banach spaces as stronger forms of the concepts of  $P$-contraction and '{C}iric type generalized $P$-contraction defined on complete metric spaces, respectively. Furthermore, the relationship between these concepts have been discussed. Finally, the uniqueness of fixed point for the presented concepts has been investigated.