Abstract:The aim of this paper is to derive some relationships between the concepts of the property of strong $(\alpha ')$ introduced recently by Hong-Kun Xu and the so-called characteristic of near convexity defined by Goebel and S\c ekowski. Particularly we provide very simple proof of a result obtained by Hong-Kun Xu.
Keywords: measure of noncompactness, near convexity, the property of strong $(\alpha ')$
AMS Subject Classification: 47H09