Some Non-linear Geometrical Properties of Banach Spaces

2014 ◽  
pp. 209-240
Author(s):  
Domingo García ◽  
Manuel Maestre
Keyword(s):  
Banach Spaces ◽  
Geometrical Properties ◽  
Non Linear

scholarly journals The non-linear geometry of Banach spaces after Nigel Kalton

2014 ◽  
Vol 44 (5) ◽  
pp. 1529-1583 ◽  
Author(s):  
G. Godefroy ◽  
G. Lancien ◽  
V. Zizler
Keyword(s):  
Banach Spaces ◽  
Non Linear ◽  
Linear Geometry

On a Theorem of Beurling and Livingston

1965 ◽  
Vol 17 ◽  
pp. 367-372 ◽  
Author(s):  
Felix E. Browder
Keyword(s):  
Banach Space ◽  
Fourier Series ◽  
Banach Spaces ◽  
General Result ◽  
Functional Equations ◽  
Linear Functional ◽  
Monotone Mappings ◽  
Conjugate Space ◽  
Non Linear ◽  
Duality Mappings

In their paper (1), Beurling and Livingston established a generalization of the Riesz-Fischer theorem for Fourier series in Lp using a theorem on duality mappings of a Banach space B into its conjugate space B*. It is our purpose in the present paper to give another proof of this theorem by deriving it from a more general result concerning monotone mappings related to recent results on non-linear functional equations in Banach spaces obtained by the writer (2, 3, 4, 5) and G. J. Minty (6).

scholarly journals Simple eigenvalues and bifurcation for a multiparameter problem

1988 ◽  
Vol 31 (1) ◽  
pp. 77-88 ◽  
Author(s):  
D. F. McGhee ◽  
M. H. Sallam
Keyword(s):  
Banach Spaces ◽  
Simple Eigenvalue ◽  
Linear Mapping ◽  
Spectral Parameters ◽  
Non Linear ◽  
Multiparameter Problem ◽  
Image Position ◽  
Bifurcation Of Solutions

We are concerned with the problem of bifurcation of solutions of a non-linear multiparameter problem at a simple eigenvalue of the linearised problem.Let X and Y be real Banach spaces, and let A, Bi, i = 1, …, n∈B(X, Y). Let : Rn × X → Y be a non-linear mapping. We consider the equationwhereand λ=(λ1, λ2,…,λn) ∈ Rn is an n-tuple of spectral parameters.

scholarly journals Non-linear dynamic response and vibration of an imperfect three-phase laminated nanocomposite cylindrical panel resting on elastic foundations in thermal environments

2017 ◽  
Vol 24 (6) ◽  
pp. 951-962 ◽  
Author(s):  
Pham Van Thu ◽  
Nguyen Dinh Duc
Keyword(s):  
Dynamic Response ◽  
Polymer Nanocomposite ◽  
Cylindrical Panel ◽  
Geometrical Properties ◽  
Elastic Foundations ◽  
Thermal Environments ◽  
Linear Dynamic ◽  
Geometrical Imperfection ◽  
Three Phase ◽  
Non Linear

AbstractThis paper presents an analytical approach to investigate the non-linear dynamic response and vibration of an imperfect three-phase laminated nanocomposite cylindrical panel resting on elastic foundations in thermal environments. Based on the classical laminated shell theory and stress function, taking into account geometrical non-linearity, initial geometrical imperfection, Pasternak-type elastic foundation, and temperature, the governing equations of the three-phase laminated nanocomposite cylindrical panel are derived. The numerical results for the dynamic response and vibration of the polymer nanocomposite cylindrical panel are obtained by using the Runge-Kutta method. The influences of fibres and nanoparticles, different fibre angles, material and geometrical properties, imperfection, elastic foundations, and temperature on the non-linear dynamic response of the polymer nanocomposite cylindrical panel are discussed in detail.

scholarly journals Homogeneous operators and essential complexes

1989 ◽  
Vol 31 (1) ◽  
pp. 73-85 ◽  
Author(s):  
F.-H. Vasilescu
Keyword(s):  
Banach Spaces ◽  
Small Perturbations ◽  
New Approach ◽  
Non Linear ◽  
Homogeneous Mappings ◽  
The Stability ◽  
Homogeneous Operators ◽  
Fredholm Complexes ◽  
Gap Topology

The aim of this work is to present a new approach to the concept of essential Fredholm complex of Banach spaces ([10], [2]; see also [11], [4], [6], [7] etc. for further connections), by using non-linear homogeneous mappings. We obtain some generalized homotopic properties of the class of essential Fredholm complexes, in our sense, which are then applied to establish its relationship with similar concepts. We also prove the stability of this class under small perturbations with respect to the gap topology.

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