DOI: 10.24193/fpt-ro.2020.2.34

Authors: Ji Gao

Abstract: Let X and X^* be a Banach space and its dual, and let B(X) and S(X) be the unit ball and unit sphere of X respectively. In this paper, we introduce a new parameter of w_n^* Separation, w_n^*(X^*), in X^* and study the relation between this parameter and normal structure in X, and the relation between packing constant P(α, X) introduced by Kottman and normal structure that implies the existence of fixed point for non-expansive mappings. Some new results about fixed points of non-expansive mapping are obtained.

Key Words and Phrases: Fixed points, normal structure, packing, ultra-product, weak normal structure.

2010 Mathematics Subject Classification: 46B20, 46C05, 52A07, 47H10.

Published on-line: July 1st, 2020.

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