منابع مشابه
The James and von Neumann-Jordan type constants and uniform normal structure in Banach spaces
Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some sufficient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper significantly generalize and improve many known results in...
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Let X be a normed linear space, and let S(X) = fx 2 X : kxk = 1g be the unit sphere of X. Brodskii and Milman 1] introduced the following geometric concept: Deenition 1. A bounded, convex subset K of a Banach space X is said to have normal structure if every convex subset H of K that contains more than one point contains a point x 0 2 H, such that supfkx 0 ? yk : y 2 Hg < d(H); where d(H) = sup...
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In this paper, we introduce parameters slε(X) and sl0(X) based on slices of Banach space X . Using these parameters we describe some new properties of Banach spaces related to normal structure, uniformly non-squareness and others. In particular, we prove that if sl 2 3 (X) < 2, then X has normal structure, and sl0(X) = ε0(X) where ε0(X) is the characteristic of convexity of X . In addition, we ...
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We obtained the estimates of Normal structure coefficient N(X) by NeumannJordan constant CNJ(X) of a Banach space X and found that X has uniform normal structure if CNJ(X) < (3 + √ 5)/4. These results improved both Prus’ [6] and Kato, Maligranda and Takahashi’s [4] work.
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1968
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1968.26.433