Vol. 104, No. 2, 1983

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Some properties of the characteristic of convexity relating to fixed point theory

David Downing and Barry Turett

Vol. 104 (1983), No. 2, 343–350
Abstract

Fixed point theorems for uniformly lipschitzian mappings often restrict the characteristic of convexity, 𝜀0(X), of the underlying Banach space to be less than one. This condition is discussed; in particular, it is shown that, for Banach spaces, 𝜀0(X) < 1 is equivalent to a condition imposed by E. A. Lifschitz in arbitrary metric spaces. The stability of this condition with respect to Banach-Mazur distance and Lebesgue-Bochner function spaces is also considered.

Mathematical Subject Classification 2000
Primary: 47H10
Secondary: 46B20
Milestones
Received: 20 April 1981
Published: 1 February 1983
Authors
David Downing
Barry Turett