scholarly journals On James and Jordan–von Neumann constants and the normal structure coefficient of Banach spaces

2001 ◽  
Vol 144 (3) ◽  
pp. 275-295 ◽  
Author(s):  
Mikio Kato ◽  
Lech Maligranda ◽  
Yasuji Takahashi
Keyword(s):  
Banach Spaces ◽  
Normal Structure ◽  
Von Neumann ◽  
Structure Coefficient

scholarly journals The generalized von Neumann--Jordan constant and normal structure in Banach spaces

2015 ◽  
Vol 6 (4) ◽  
pp. 206-214 ◽  
Author(s):  
Xi Wang ◽  
Yunan Cui ◽  
Chiping Zhang
Keyword(s):  
Banach Spaces ◽  
Normal Structure ◽  
Von Neumann

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 Hölder’s means and fixed points for multivalued nonexpansive mappings

Filomat ◽  
2018 ◽  
Vol 32 (19) ◽  
pp. 6531-6547
Author(s):  
Mina Dinarvand
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Recent Literature ◽  
Nonexpansive Mappings ◽  
Convergent Sequence ◽  
Normal Structure ◽  
James Constant ◽  
Von Neumann ◽  
Geometric Conditions ◽  
Weakly Convergent Sequence Coefficient

In this paper, we show some geometric conditions on Banach spaces by considering H?lder?s means and many well known parameters namely the James constant, the von Neumann-Jordan constant, the weakly convergent sequence coefficient, the normal structure coefficient, the coefficient of weak orthogonality, which imply the existence of fixed points for multivalued nonexpansive mappings and normal structure of Banach spaces. Some of our main results improve and generalize several known results in the recent literature on this topic. We also show that some of our results are sharp.

scholarly journals The von Neumann-Jordan constant, weak orthogonality and normal structure in Banach spaces

2005 ◽  
Vol 134 (02) ◽  
pp. 355-364 ◽  
Author(s):  
Antonio Jiménez-Melado ◽  
Enrique Llorens-Fuster ◽  
Satit Saejung
Keyword(s):  
Banach Spaces ◽  
Normal Structure ◽  
Von Neumann

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 Some Properties Concerning the JL(X) and YJ(X) Which Related to Some Special Inscribed Triangles of Unit Ball

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1285
Author(s):  
Asif Ahmad ◽  
Yuankang Fu ◽  
Yongjin Li
Keyword(s):  
Unit Ball ◽  
Banach Spaces ◽  
Uniformly Convex ◽  
Geometric Properties ◽  
James Constant ◽  
Von Neumann ◽  
Geometric Constants

In this paper, we will make some further discussions on the JL(X) and YJ(X) which are symmetric and related to the side lengths of some special inscribed triangles of the unit ball, and also introduce two new geometric constants L1(X,▵), L2(X,▵) which related to the perimeters of some special inscribed triangles of the unit ball. Firstly, we discuss the relations among JL(X), YJ(X) and some geometric properties of Banach spaces, including uniformly non-square and uniformly convex. It is worth noting that we point out that uniform non-square spaces can be characterized by the side lengths of some special inscribed triangles of unit ball. Secondly, we establish some inequalities for JL(X), YJ(X) and some significant geometric constants, including the James constant J(X) and the von Neumann-Jordan constant CNJ(X). Finally, we introduce the two new geometric constants L1(X,▵), L2(X,▵), and calculate the bounds of L1(X,▵) and L2(X,▵) as well as the values of L1(X,▵) and L2(X,▵) for two Banach spaces.

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