Property($K^{\ast }$) Implies $R(X)\le 1+\frac{1}{1+r_{X^{\ast }}(1)}$

Abstract

It is shown that if the dual of a Banach space satisfies Property($K^{\ast }$) then $R(X)\le 1+\frac{1}{1+r_{X^{\ast }}(1)}<2$ where $r_{X^{\ast }}(c)$ is Opial's modulus for $X^{\ast }.$ Thus $X$ has the weak fixed point property.

arXiv commentarXiv admin note: text overlap with arXiv:2007.00942