Displaying similar documents to “Fixed point free maps of a closed ball with small measures of noncompactness.”

Averages of uniformly continuous retractions

A. Jiménez-Vargas, J. Mena-Jurado, R. Nahum, J. Navarro-Pascual (1999)

Studia Mathematica

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Let X be an infinite-dimensional complex normed space, and let B and S be its closed unit ball and unit sphere, respectively. We prove that the identity map on B can be expressed as an average of three uniformly retractions of B onto S. Moreover, for every 0≤ r < 1, the three retractions are Lipschitz on rB. We also show that a stronger version where the retractions are required to be Lipschitz does not hold.

Spaces of Lipschitz and Hölder functions and their applications.

Nigel J. Kalton (2004)

Collectanea Mathematica

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We study the structure of Lipschitz and Hölder-type spaces and their preduals on general metric spaces, and give applications to the uniform structure of Banach spaces. In particular we resolve a problem of Weaver who asks wether if M is a compact metric space and 0 &lt; α &lt; 1, it is always true the space of Hölder continuous functions of class α is isomorphic to l. We show that, on the contrary, if M is a compact convex subset of a Hilbert space this isomorphism holds if...

Some Applications of Simons’ Inequality

Godefroy, Gilles (2000)

Serdica Mathematical Journal

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We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.