scholarly journals Sufficient conditions for uniform normal structure of Banach spaces and their duals

2007 ◽  
Vol 330 (1) ◽  
pp. 597-604 ◽  
Author(s):  
Satit Saejung
Keyword(s):  
Banach Spaces ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
Uniform Normal Structure

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 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 The fixed point property and normal structure for some B-convex Banach spaces

2001 ◽  
Vol 63 (1) ◽  
pp. 75-81 ◽  
Author(s):  
Jesús García-Falset ◽  
Enrique Llorens-Fuster ◽  
Eva M. Mazcuñán-Navarro
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
Fixed Point Property ◽  
Sufficient Condition ◽  
Point Property

We give a sufficient condition for normal structure more general than the well known ɛ0(X) < 1. Moreover we obtain sufficient conditions for the fixed point property for some B-convex Banach spaces.

scholarly journals Some Inequalities Concerning the Weakly Convergent Sequence Coefficient in Banach Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-8
Author(s):  
Hongwei Jiao ◽  
Yunrui Guo
Keyword(s):  
Banach Spaces ◽  
Sufficient Conditions ◽  
Convergent Sequence ◽  
Normal Structure ◽  
Weakly Convergent Sequence Coefficient

We establish two inequalities concerning the weakly convergent sequence coefficient and other parameters, which enable us to obtain some sufficient conditions for normal structure.

scholarly journals New Geometric Constants in Banach Spaces Related to the Inscribed Equilateral Triangles of Unit Balls

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 951
Author(s):  
Yuankang Fu ◽  
Qi Liu ◽  
Yongjin Li
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
Upper And Lower Bounds ◽  
Uniformly Convex ◽  
Equilateral Triangles ◽  
Geometric Constant ◽  
Geometric Constants

Geometric constant is one of the important tools to study geometric properties of Banach spaces. In this paper, we will introduce two new geometric constants JL(X) and YJ(X) in Banach spaces, which are symmetric and related to the side lengths of inscribed equilateral triangles of unit balls. The upper and lower bounds of JL(X) and YJ(X) as well as the values of JL(X) and YJ(X) for Hilbert spaces and some common Banach spaces will be calculated. In addition, some inequalities for JL(X), YJ(X) and some significant geometric constants will be presented. Furthermore, the sufficient conditions for uniformly non-square and normal structure, and the necessary conditions for uniformly non-square and uniformly convex will be established.

scholarly journals Existence And Controllability Results For Fractional Control Systems In Reflexive Banach Spaces Using Fixed Point Theorem

2020 ◽  
Vol 17 (4) ◽  
pp. 1283
Author(s):  
Naseif Jasim AL-Jawari
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonexpansive Mapping ◽  
Control Systems ◽  
Banach Spaces ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
Reflexive Banach Spaces ◽  
Fractional Control

       In this paper, a fixed point theorem of nonexpansive mapping is established to study the existence and sufficient conditions for the controllability of nonlinear fractional control systems in reflexive Banach spaces. The result so obtained have been modified and developed in arbitrary space having Opial’s condition by using fixed point theorem deals with nonexpansive mapping defined on a set has normal structure. An application is provided to show the effectiveness of the obtained result.

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.

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