Best Proximity point for Z-contraction and Suzuki type Z-contraction mappings with an application to fractional calculus

• Main Authors: Somayya Komal, Poom Kumam, Dhananjay Gopal
• Format: Article
• Language: English
• Published: Universitat Politècnica de València 2016-10-01
• Series: Applied General Topology
• Subjects: best proximity point; weak $P$-property; Suzuki type $\mathcal{Z}$-contraction; functional differential equation.
• Online Access: http://polipapers.upv.es/index.php/AGT/article/view/5660

In this article, we introduced the best proximity point theorems for $\mathcal{Z}$-contraction and Suzuki type $\mathcal{Z}$-contraction in the setting of complete metric spaces. Also by the help of weak $P$-property and $P$-property, we proved existence and uniqueness of best proximity point. There is a simple example to show the validity of our results. Our results extended and unify many existing results in the literature. Moreover, an application to fractional order functional differential equation is discussed.