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 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 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 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 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.

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

2020 ◽  
Vol 4 (2) ◽  
pp. 104-115
Author(s):  
Khalil Ezzinbi ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Mönch Fixed Point Theorem ◽  
The Resolvent Operator

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

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