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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:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H07Monotone and positive operators on ordered topological linear spaces
45G99Nonlinear integral equations