On some Banach space properties sufficient for normal structure

Abstract

In this paper, we present some sufficient conditions for which a Banach space has normal structure and therefore the fixed point property for nonexpansive mappings in terms of the generalized James, von Neumann-Jordan, Zbȃganu constants, the Ptolemy constant and the Domínguez-Benavides coefficient. Our main results extend and improve some known results in the recent literature.

On a General Class of Geometric Constants and Normal Structure in Banach Spaces

“…Since then, many mathematicians have established that, under various geometric properties of a Banach space often measured by different geometric constants, normal structure or uniform normal structure of the space is guaranteed. For more details in this direction, we refer the reader to [10,11,12,13,14,15,16,17,21,25,28,29,30,31,32,36] and the references mentioned therein.…”

On von Neumann-Jordan type constant and sufficient conditions for fixed points of multivalued nonexpansive mappings

“…Both the James constant J(X) and the von Neumann-Jordan constant C N J (X) play an important role in the description of various geometric structures. Therefore, many recent studies have focused on these constants (see [3,4,5,6,7,8,10,11,15,16,20,23,25,26]). S. Dhompongsa et al [5] introduced the Domínguez-Lorenzo condition ((DL)-condition, in short) which implies weak normal structure of a Banach space and the fixed point property for multivalued nonexpansive mappings.…”