On Some Coupled Quasi-fixed Points Theorems

Some existence theorems are known for coupled quasi-fixed points of nonlinear mixed monotone operators from a k-fold conical segmentwu0, ¨0xinto a real Banach space, where ks1 or 2. In this note, we extend those results to an arbitrary but finite k by a simple but nontrivial iterative mechanism. Interestingly enough, for mixed monotone operators with kG3 folds, the Lipschitz condition ensuring the uniqueness of their fixed points is as simple as the cases of kF2