Original Article
Kyungpook Mathematical Journal 2014; 54(3): 485-500
Published online September 23, 2014
Copyright © Kyungpook Mathematical Journal.
A Coupled Fixed Point Theorem for Mixed Monotone Mappings on Partial Ordered $G$-Metric Spaces
Hosoo Lee
College of Basic Studies, Yeungnam University, 280 Daehak-Ro, Gyengsan Gyengbook, 712-749 Korea
In this paper, we establish coupled fixed point theorems for mixed monotone mappings satisfying nonlinear contraction involving a pair of altering distance functions in ordered $G$-metric spaces. Via presented theorems we extend and generalize the results of Harjani et al. [J. Harjani, B. L'{o}pez and K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Anal. 74 (2011) 1749-1760] and Choudhury and Maity [B.S. Choudhury and P. Maity, Coupled fixed point results in generalized metric spaces. Math. Comput. Model. 54 (2011), 73-79].
Keywords: Fixed point, mixed monotone property, { iny $G$}-metric space