scholarly journals Schäffer-type constant and uniform normal structure in Banach spaces

2016 ◽  
Vol 7 (3) ◽  
pp. 452-461
Author(s):  
Zhan-fei Zuo ◽  
Chun-lei Tang
Keyword(s):  
Banach Spaces ◽  
Normal Structure ◽  
Uniform Normal Structure

scholarly journals Generalised Jordan-von Neumann constants and uniform normal structure

2003 ◽  
Vol 67 (2) ◽  
pp. 225-240 ◽  
Author(s):  
S. Dhompongsa ◽  
P. Piraisangjun ◽  
S. Saejung
Keyword(s):  
Banach Spaces ◽  
Normal Structure ◽  
Von Neumann ◽  
Uniform Normal Structure

We introduce a new geometric coefficient related to the Jordan-von Neumann constant. This leads to improved versions of known results and yields new ones on super-normal structure for Banach spaces.

scholarly journals Some examples concerning normal and uniform normal structure in Banach spaces

1990 ◽  
Vol 48 (2) ◽  
pp. 223-234 ◽  
Author(s):  
Mark A. Smith ◽  
Barry Turett
Keyword(s):  
Banach Spaces ◽  
Normal Structure ◽  
Quotient Spaces ◽  
Dual Property ◽  
Uniform Normal Structure ◽  
Uniform Rotundity

AbstractExamples are given that show the following: (1) normal structure need not be inherited by quotient spaces; (2) uniform normal structure is not a self-dual property; and (3) no degree of k–uniform rotundity need be present in a space with uniform normal structure.

scholarly journals Uniform asymptotic normal structure, the uniform semi-Opial property and fixed points of asymptotically regular uniformly lipschitzian semigroups. Part I

1998 ◽  
Vol 3 (1-2) ◽  
pp. 133-151 ◽  
Author(s):  
Monika Budzyńska ◽  
Tadeusz Kuczumow ◽  
Simeon Reich
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Normal Structure ◽  
Opial Property ◽  
Uniform Normal Structure ◽  
Asymptotic Normal ◽  
Asymptotically Regular

In this paper we introduce the uniform asymptotic normal structure and the uniform semi-Opial properties of Banach spaces. This part is devoted to a study of the spaces with these properties. We also compare them with those spaces which have uniform normal structure and with spaces withWCS(X)>1.

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 On the modulus ofU-convexity

2005 ◽  
Vol 2005 (1) ◽  
pp. 59-66 ◽  
Author(s):  
Satit Saejung
Keyword(s):  
Banach Space ◽  
Dual Space ◽  
Normal Structure ◽  
Uniform Normal Structure

We prove that the moduli ofU-convexity, introduced by Gao (1995), of the ultrapowerX˜of a Banach spaceXand ofXitself coincide wheneverXis super-reflexive. As a consequence, some known results have been proved and improved. More precisely, we prove thatuX(1)>0implies that bothXand the dual spaceX∗ofXhave uniform normal structure and hence the “worth” property in Corollary 7 of Mazcuñán-Navarro (2003) can be discarded.

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
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