scholarly journals Renormings of Nonseparable Reflexive Banach Spaces and Diametrically Complete Sets with Empty Interior

2020 ◽  
Author(s):  
Wiesława Kaczor ◽  
Tadeusz Kuczumow ◽  
Simeon Reich ◽  
Mariola Walczyk
Keyword(s):  
Banach Spaces ◽  
Empty Interior ◽  
Reflexive Banach Spaces ◽  
Complete Sets

Existence of diametrically complete sets with empty interior in reflexive and separable Banach spaces

2020 ◽  
Vol 278 (7) ◽  
pp. 108418
Author(s):  
Monika Budzyńska ◽  
Tadeusz Kuczumow ◽  
Simeon Reich ◽  
Mariola Walczyk
Keyword(s):  
Banach Spaces ◽  
Empty Interior ◽  
Complete Sets

scholarly journals Generalized Uniqueness Theorem for Ordinary Differential Equations in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Ezzat R. Hassan ◽  
M. Sh. Alhuthali ◽  
M. M. Al-Ghanmi
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Uniqueness Theorem ◽  
Banach Spaces ◽  
Nonlinear Ordinary Differential Equations ◽  
Empty Interior ◽  
Reflexive Banach Spaces ◽  
Uniqueness Criterion ◽  
The Cauchy Problem

We consider nonlinear ordinary differential equations in Banach spaces. Uniqueness criterion for the Cauchy problem is given when any of the standard dissipative-type conditions does apply. A similar scalar result has been studied by Majorana (1991). Useful examples of reflexive Banach spaces whose positive cones have empty interior has been given as well.

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