# A new fixed point result via property P with an application

Volume 10, Issue 4, pp 2066--2078
Publication Date: April 20, 2017 Submission Date: January 27, 2017
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### Authors

Z. Mustafa - Department of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar. - Department of Mathematics, The Hashemite University, P. O. 330127, Zarqa 13115, Jordan. M. M. M. Jaradat - Department of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar. E. Karapinar - Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, AU, 21589, Jeddah, Saudi Arabia. - Department of Mathematics, Atilim University 06836, Incek, Ankara, Turkey.

### Abstract

The purpose of this paper is to introduce a new contractive condition. We prove the existence and uniqueness of a fixed point of self-mapping under this new contractive condition. Moreover, we observe analog of these results for the mappings that satisfy the property P. An application on integral equations is presented to illustrate the main result. Our results extend and generalize well-known results in the literature.

### Keywords

• Contractive mapping
• fixed point
• partial metric space
• property P
• integral equations.

•  46T99
•  47H10
•  54H25

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