Abstract
We consider two Pythagorean modulus introduced by Gao (2005, 2006) recently. The exact values concerning these modulus for some classical Banach spaces are determined. Some applications in geometry of Banach spaces are also obtained.
Highlights
Gao introduced some moduli from Pythagorean theorem
In terms of these moduli, he got some sufficient conditions for a Banach space X to have uniform normal structure, which plays an import role in fixed-point theory
Following Gao, we study the further properties concerning the Pythagorean moduli
Summary
Gao introduced some moduli from Pythagorean theorem. In terms of these moduli, he got some sufficient conditions for a Banach space X to have uniform normal structure, which plays an import role in fixed-point theory. For every nonnegative number , the Pythagorean moduli are given by [1, 2]. Following Gao, we study the further properties concerning the Pythagorean moduli. We find that these moduli are connected with some geometric properties. They enable us to distinguish several important classes of spaces such as uniformly convex, uniformly smooth, or uniformly nonsquare
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