0000000000662082

AUTHOR

Brailey Sims

showing 2 related works from this author

Fixed point theory for almost convex functions

1998

Traditionally, metric fixed point theory has sought classes of spaces in which a given type of mapping (nonexpansive, assymptotically or generalized nonexpansive, uniformly Lipschitz, etc.) from a nonempty weakly compact convex set into itself always has a fixed point. In some situations the class of space is determined by the application while there is some degree of freedom in constructing the map to be used. With this in mind we seek to relax the conditions on the space by considering more restrictive types of mappings.

Convex analysisLeast fixed pointPure mathematicsApplied MathematicsMathematical analysisConvex setSubderivativeAbsolutely convex setFixed pointKakutani fixed-point theoremFixed-point propertyAnalysisMathematics
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Property (M) and the weak fixed point property

1997

It is shown that in Banach spaces with the property (M) of Kalton, nonexpansive self mappings of nonempty weakly compact convex sets necessarily have fixed points. The stability of this conclusion under renormings is examined and conditions for such spaces to have weak normal structure are considered.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsApproximation propertyApplied MathematicsGeneral MathematicsTopological tensor productEberlein–Šmulian theoremBanach spaceUniformly convex spaceFixed-point propertyOpial propertyInterpolation spaceMathematicsProceedings of the American Mathematical Society
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