Modules of convexity, characteristic of convexity and fixed point theorems
Various numerical parameters have been introduced to describe the geometric structure of a Banach space E; classical examples are the modulus of convexity \(\delta\) (E;\(\epsilon)\), the characteristic of convexity \(\epsilon_ 0(E)\), and the normal structure coefficient N(E). For instance, if \(\epsilon_ 0(E)=0\) \([\epsilon_ 0(E)<1,\epsilon_ 0(E)<2,N(E)>1\), resp.], then E is uniformly convex [has normal structure, is reflexive, has normal structure and is reflexive, resp.]. In the present paper, the authors define corresponding characteristic \(\delta\) (C;\(\epsilon)\), \(\epsilon_ 0(C)\), and N(C) for arbitrary convex subsets C of E, and prove some fixed point theorems. This extends previous work of W. L. Bynum, K. Goebel, V. I. Gurarij, E. Moluta, E. Casini, and others.
scientific article; zbMATH DE number 4067690