Coupled fixed-point theorems for contraction mapping induced by cone ball-metric in partially ordered spaces
1 Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, 10140, Thailand
2 Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju, 660-701, Korea
Fixed Point Theory and Applications 2012, 2012:128 doi:10.1186/1687-1812-2012-128Published: 3 August 2012
Recently, Chen et al. (Appl. Math. Lett. 25:692-697, 2012) introduced the concept of the cone ball-metric and studied the common fixed-point theorems for the stronger Meir-Keeler cone-type function in cone ball-metric spaces. The purpose of this paper is to establish the coupled fixed-point theorems for nonlinear contraction mappings, which have a mixed monotone property by using the cone ball-metric. Also, we give some examples to validate our main results. At the end of this paper, we give an open problem for further investigation.
MSC: 47H10, 54H25.