A geometrical constant and normal normal structure in Banach Spaces

Recently, we introduced a new coefficient as a generalization of the modulus of smoothness and Pythagorean modulus such as J X , p ( t ). In this paper, We can compute the constant J X , p (1) under the absolute normalized norms on ℝ 2 by means of their corresponding continuous convex functions on [...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2011; no. 1; pp. 1 - 10
Main Author Zuo, Zhanfei
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 23.06.2011
Springer Nature B.V
BioMed Central Ltd
SpringerOpen
Subjects
Absolute normalized norm
Analysis
Applications of Mathematics
Banach space
Classification
Coefficients
Geometrical constant
Inequalities
Lorentz sequence space
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Norms
Smoothness
Uniform normal structure
Lorentz sequence space
Geometrical constant
Absolute normalized norm
Uniform normal structure
Online AccessGet full text
ISSN1029-242X
1025-5834
1029-242X
DOI10.1186/1029-242X-2011-16

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Summary:Recently, we introduced a new coefficient as a generalization of the modulus of smoothness and Pythagorean modulus such as J X , p ( t ). In this paper, We can compute the constant J X , p (1) under the absolute normalized norms on ℝ 2 by means of their corresponding continuous convex functions on [0, 1]. Moreover, some sufficient conditions which imply uniform normal structure are presented. 2000 Mathematics Subject Classification : 46B20.
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/1029-242X-2011-16