scholarly journals Separated sets and Auerbach systems in Banach spaces

2020 ◽  
Vol 373 (10) ◽  
pp. 6961-6998 ◽  
Author(s):  
Petr Hájek ◽  
Tomasz Kania ◽  
Tommaso Russo
Keyword(s):  
Banach Spaces ◽  
Separated Sets

scholarly journals Large separated sets of unit vectors in Banach spaces of continuous functions

2019 ◽  
Vol 157 (2) ◽  
pp. 173-187
Author(s):  
Marek Cúth ◽  
Ondřej Kurka ◽  
Benjamin Vejnar
Keyword(s):  
Banach Spaces ◽  
Continuous Functions ◽  
Spaces Of Continuous Functions ◽  
Separated Sets ◽  
Unit Vectors

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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