Existence and uniqueness of fixed points for some mixed monotone operators. (English) Zbl 1229.47082
Summary: We introduce the notion of \(e\)-concave-convex operator. Without any compactness or continuity assumptions, we prove the existence and uniqueness of fixed points, giving monotone iterative sequences for the unique fixed point of the operator. Finally, we apply the results to an integral equation of polynomial type which possesses items of measurable functions.
MSC:
| 47H10 | Fixed-point theorems |
| 47H07 | Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces |
| 45G99 | Nonlinear integral equations |
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