Normal structure and some geometric parameters related to the modulus of U-convexity in banach spaces

2011 ◽  
Vol 31 (3) ◽  
pp. 1035-1040
Author(s):  
Ji Gao ◽  
Satit Saejung
Keyword(s):  
Banach Spaces ◽  
Normal Structure ◽  
Geometric Parameters

scholarly journals Modulus of Convexity, the CoeffcientR(1,X), and Normal Structure in Banach Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-5 ◽  
Author(s):  
Hongwei Jiao ◽  
Yunrui Guo ◽  
Fenghui Wang
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Normal Structure ◽  
Geometric Parameters ◽  
Sufficient Condition ◽  
Modulus Of Convexity

LetδX(ϵ)andR(1,X)be the modulus of convexity and the Domínguez-Benavides coefficient, respectively. According to these two geometric parameters, we obtain a sufficient condition for normal structure, that is, a Banach spaceXhas normal structure if2δX(1+ϵ)>max{(R(1,x)-1)ϵ,1-(1-ϵ/R(1,X)-1)}for someϵ∈[0,1]which generalizes the known result by Gao and Prus.

scholarly journals On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 116
Author(s):  
Qi Liu ◽  
Yongjin Li
Keyword(s):  
Banach Spaces ◽  
Product Space ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
The Other ◽  
Inner Product ◽  
Equivalent Characterization ◽  
Geometric Constant ◽  
Geometric Constants

In this paper, we will introduce a new geometric constant LYJ(λ,μ,X) based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and LYJ(λ,μ,X). Also, this new coefficient is computed for X being concrete space.

scholarly journals Normal structure in Banach spaces

1968 ◽  
Vol 26 (3) ◽  
pp. 433-440 ◽  
Author(s):  
Lawrence Belluce ◽  
William Kirk ◽  
Eugene Steiner
Keyword(s):  
Banach Spaces ◽  
Normal Structure

Normal Structure for Banach Spaces with Schauder Decomposition

1989 ◽  
Vol 32 (3) ◽  
pp. 344-351 ◽  
Author(s):  
M. A. Khamsi
Keyword(s):  
Banach Spaces ◽  
Normal Structure

AbstractWe introduce a new constant in Banach spaces which implies, in certain cases, the weak- or weak*-normal structure.

scholarly journals Weak Normal Structure in Banach Spaces with Symmetric Norm

1999 ◽  
Vol 236 (1) ◽  
pp. 38-47
Author(s):  
Helga Fetter ◽  
Berta Gamboa de Buen
Keyword(s):  
Banach Spaces ◽  
Normal Structure

scholarly journals On Semi-Uniform Kadec-Klee Banach Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Satit Saejung ◽  
Ji Gao
Keyword(s):  
Banach Spaces ◽  
Normal Structure ◽  
Direct Sum

Inspired by the concept ofU-spaces introduced by Lau, (1978), we introduced the class of semi-uniform Kadec-Klee spaces, which is a uniform version of semi-Kadec-Klee spaces studied by Vlasov, (1972). This class of spaces is a wider subclass of spaces with weak normal structure and hence generalizes many known results in the literature. We give a characterization for a certain direct sum of Banach spaces to be semi-uniform Kadec-Klee and use this result to construct a semi-uniform Kadec-Klee space which is not uniform Kadec-Klee. At the end of the paper, we give a remark concerning the uniformly alternative convexity or smoothness introduced by Kadets et al., (1997).

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