Nonself KKM Maps and Corresponding Theorems in Hadamard Manifolds

Parin Chaipunya; Poom Kumam

doi:10.4995/agt.2015.2305

Authors

Parin Chaipunya King Mongkut's University of Technology Thonburi
Poom Kumam King Mongkut's University of Technology Thonburi

DOI:

https://doi.org/10.4995/agt.2015.2305

Keywords:

KKM Maps, Hadamard manifolds, generalized equilibrium problems, best proximity points

Abstract

In this paper, we consider the KKM maps defined for a nonself map and the correlated intersection theorems in Hadamard manifolds. We also study some applications of the intersection results. Our outputs improved the results of Raj and Somasundaram [17, V. Sankar Raj and S. Somasundaram, KKM-type theorems for best proximity points, Appl. Math. Lett., 25(3): 496–499, 2012.].

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Author Biographies

Parin Chaipunya, 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

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