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Some properties of
the characteristic of convexity relating to fixed point
theory
David Downing and Barry Turett |
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Vol. 104 (1983), No. 2, 343–350
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Abstract |
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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
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Milestones
Received: 20 April 1981
Published: 1 February 1983
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Authors |
| David Downing | |
| Barry Turett | |
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