Applicable Analysis · 1990 · 101 citations · 6 references
Natural SciencesMathematicsBrake SystemsDifferential EquationsTemporary Anchorage DevicesExistence TheoremsExistence TheoryFixed Point TheoryFixed PointsInitial Value ProblemsOperator TheoryBanach Fixed Point TheoremCompactness TheoremsConvexityConvexity AnalysisExistence Of Fixed PointsFixed Point PropertyMonotone MappingsOperator Monotonicity
In this paper, we prove some fixed point theorems of increasing operators which map an order interval into itself. Compactness conditions on the operator are removed by assuming the space to be weakly complete or assuming the operator to have some concavity or convexity properties. some results of M. A. Krasnoselskii and H. Amann are generalized. The abstract results are used to get some existence theorems for ODEs in Banach spaces.
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Positive Solutions of Operator Equations.
A. R. Brodsky, M. A. Krasnosel’skii, Richard E. Flaherty et al. · American Mathematical Monthly · 1967 · 2.1K citations
On fundamental properties of a Banach space with a cone
Tsuyoshi Andô · Pacific Journal of Mathematics · 1962 · 121 citations · Full text