Some properties of the characteristic of convexity relating to fixed point theory
David J. Downing, Jay Turett · Pacific Journal of Mathematics · 1983
Fixed point theorems for uniformly lipschitzian mappings often restrict the characteristic of convexity, ε o (X), of the underlying Banach space to be less than one.This condition is discussed; in particular, it is shown that, for Banach spaces, ε o (x) < 1 is equivalent to a condition imposed by E. A. Lif schitz in arbitrary metric spaces.The stability of this condition with respect to Banach-Mazur distance and Lebesgue-Bochner function spaces is also considered.