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Directional moduli of rotundity and smoothness. (English) Zbl 1060.46501
From the author’s introduction: The authors provide a systematic survey of what can be said about spaces with various types of rotund norms whose associated modulus of rotundity is of power type, in particular we give a directional improvement of the result of R. Deville, G. Godefroy and V. Zizler [Mathematika 40, 305-321 (1993; Zbl 0792.46007)] by combining their ideas with a dual version of an argument of J. M. Borwein and D. Noll [Trans. Am. Math. Soc. 342, 43-81 (1994; Zbl 0802.46027)]. Some related results concerning directional moduli of smoothness of power type are also considered. A relationship of some directional moduli of smoothness to normal structure is discussed.
46B20 Geometry and structure of normed linear spaces
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