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

Somayya Komal; Poom Kumam; Dhananjay Gopal

doi:10.4995/agt.2016.5660

Authors

Somayya Komal King Mongkut's University of Technology Thonburi
Poom Kumam King Mongkut's University of Technology Thonburi
Dhananjay Gopal SV National Institute of Technology

DOI:

https://doi.org/10.4995/agt.2016.5660

Keywords:

best proximity point, weak P-property, Suzuki type Z-contraction, functional differential equation

Abstract

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.

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Author Biographies

Somayya Komal, King Mongkut's University of Technology Thonburi

Department of Mathematics, Faculty of Science

Poom Kumam, King Mongkut's University of Technology Thonburi

Poom Kumam received his B.S. degree in mathematics education from the Burapha University, Chonburi, Thailand, in 2000, his M.S. degree (mathematics) from the Chiang Mai University, Chiang Mai, Thailand, in 2002, under the supervision of Professor Sompong Dhompongsa, and his Ph.D. degree (mathematics) from the Naresuan University, Phitsanulok, Thailand, in 2007, under the supervision of Professor Somyot Plubtieng. He started his career as a Lecturer at the Department of Mathematics, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand, in 2002. In 2008, he received a grant from Franco-Thai Cooperation for short-term research at Laboratoire de Mathématiques, Université de Bretagne Occidentale, France. Furthermore, in 2011, Kumam had an opportunity to take a role as a Visiting Professor at Kyungnam University and Gyeongsang National University, Republic of Korea. In 2012, he took the same role, a Visiting Professor, at the University of Alberta, AB, Canada. He won two of the most important awards for mathematicians. The first one is the TRF-CHE-Scopus Young Researcher Award in 2010 which is the award given by the corporation from three organizations: Thailand Research Fund (TRF), the Commission of Higher Education (CHE), and Elsevier Publisher (Scopus). The second award was in 2012 when he received TWAS Prize for Young Scientist in Thailand which is given by the Academy of Sciences for the Developing World TWAS (UNESCO) together with the National Research Council of Thailand. His research interest focuses on fixed-point theory in both pure science and applied science.

Biography Updated on 13 November 2013

Dhananjay Gopal, SV National Institute of Technology

Department of applied Mathematics and Humanities

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