scholarly journals Vanishing of cohomology with coefficients in representations on Banach spaces of groups acting on buildings

2017 ◽  
Vol 92 (2) ◽  
pp. 389-428 ◽  
Author(s):  
Izhar Oppenheim
Keyword(s):  
Banach Spaces ◽  
Vanishing Of Cohomology

scholarly journals Cohomology of deformations

2014 ◽  
Vol 07 (01) ◽  
pp. 81-104 ◽  
Author(s):  
Uri Bader ◽  
Piotr W. Nowak
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Linear Part ◽  
Quantitative Estimates ◽  
Fixed Point Properties ◽  
Vanishing Of Cohomology ◽  
Uniformly Bounded ◽  
Affine Actions

In this paper we study cohomology of a group with coefficients in representations on Banach spaces and its stability under deformations. We show that small, metric deformations of the representation preserve vanishing of cohomology. As applications we obtain deformation theorems for fixed point properties on Banach spaces. In particular, our results yield fixed point theorems for affine actions in which the linear part is not uniformly bounded. Our proofs are effective and allow for quantitative estimates.

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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