In this paper, we extend and complement some recent results of coupled fixed point theorems of Luong and Thuan in [N. V. Luong, N. X. Thuan, Coupled fixed point theorems for mixed monotone mappings and an application to integral equations, Computers and Mathematics with Applications 62 (2011) 4238-4248.] by weaken the concept of the mixed monotone property. The example of a nonlinear contraction mapping which is not applied by the results of Luong and Thuan, but can be applied to our results is given. The presented results extend and complement results of Luong and Thuan and some known existence results from the literature.
"Coupled fixed point theorems for $F$-invariant set,"
Applied Mathematics & Information Sciences: Vol. 07:
1, Article 31.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss1/31