Abstract
Some existence theorems are known for coupled quasi-fixed points of nonlinear mixed monotone operators from a k-fold conical segment [u0, u0] into a real Banach space, where k = 1 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 k ≥ 3 folds, the Lipschitz condition ensuring the uniqueness of their fixed points is as simple as the cases of k ≤ 2.
Original language | English |
---|---|
Pages (from-to) | 444-450 |
Number of pages | 7 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 204 |
Issue number | 2 |
DOIs | |
State | Published - 01 12 1996 |
Externally published | Yes |