Fixed points, normal structure and moduli of semi-UKK, semi-NUC and semi-UKK spaces

Khader, M.M.; Saejung, Satit; Gao, Ji

doi:10.1016/j.joems.2014.01.004

Fixed points, normal structure and moduli of semi-UKK, semi-NUC and semi-UKK spaces

Document Type : Original Article

Authors

¹ Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt

² Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

³ Department of Mathematics, Community College of Philadelphia, Philadelphia, PA 19130-3991, USA

10.1016/j.joems.2014.01.004

Abstract

Let X and X be a Banach space and its dual. In this paper a new kind of separation measure, u-separation, is introduced. The new kind of Banach spaces: semi-UKK and semi-NUC, and
modulus of semi-UKK and modulus of semi-NUC are introduced in terms of this u-separation
measure. The relationships of these moduli with normal structure, reflexivity and other convex
properties are studied respectively. Many known results for fixed points of nonexpansive mappings
are improved upon. The u-separation measure and its properties in X are also defined and studied.

Keywords