### A CONSTANT RELATED TO FIXED POINTS AND NORMAL STRUCTURE IN BANACH SPACES

#### Abstract

Let X be a Banach space and S_X = {x in X : ||x|| = 1} be the unit sphere of X.

The parameter

V_X^* (\epsilon) = sup { 1- \frac{||x+y||}{2} : x,y in S_X and <x-y, f> <= \varepsilon for some f in \triangledown_x },

where 0 <= \varepsilon <= 2 and \triangledown_x \subseteq S_X^* is the set of norm 1 supporting functionals f at x, is

introduced and investigated. The main result is that if V_X^* < \frac{ \varepsilon }{2} for some 0 < \varepsilon < 2, then

X is uniformly nonsquare and has a uniform normal structure.

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**ISSN: 1229-1595 (Print), 2466-0973 (Online)**

## Comments on this article

by Anderson Aragão (2017-12-21)

by Anderson Aragão (2017-12-21)