Computation of certain continuous integrals in the space of continuous functions defined on a compact set

1993 ◽  
Vol 66 (6) ◽  
pp. 2579-2582
Author(s):  
I. M. Koval'chik
Keyword(s):  
Continuous Functions ◽  
Compact Set ◽  
Space Of Continuous Functions

scholarly journals Compactness of the Set of Trajectories of the Control System Described by a Urysohn Type Integral Equation

2016 ◽  
Vol 7 (1) ◽  
pp. 59-65 ◽  
Author(s):  
Nesir Huseyin
Keyword(s):  
Integral Equation ◽  
Control System ◽  
Admissible Control ◽  
Continuous Functions ◽  
Closed Ball ◽  
Compact Set ◽  
Control Vector ◽  
Space Of Continuous Functions ◽  
Control Functions ◽  
Type Integral

The control system with integralconstraint on the controls is studied, where the behavior of the system by a Urysohn type integral equation is described.  It is assumed thatthe system is nonlinear with respect to the state vector, affine with respect to the control vector.  The closed ball ofthe space $L_p(E;\mathbb{R}^m)$ $(p>1)$ with radius $r$ and centered at theorigin, is chosen as the set of admissible control functions, where $E\subset \mathbb{R}^k$ is a compact set. Itis proved that the set of trajectories generated by all admissible control functions is a compact subset of the space of continuous functions.

Some properties of the space of fuzzy-valued continuous functions on a compact set

2009 ◽  
Vol 160 (11) ◽  
pp. 1620-1631 ◽  
Author(s):  
Jin-Xuan Fang ◽  
Qiong-Yu Xue
Keyword(s):  
Continuous Functions ◽  
Compact Set

Periodic solutions to functional differential equations

1985 ◽  
Vol 101 (3-4) ◽  
pp. 253-271 ◽  
Author(s):  
O. A. Arino ◽  
T. A. Burton ◽  
J. R. Haddock
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Continuous Functions ◽  
Ultimate Boundedness ◽  
Space Of Continuous Functions ◽  
Uniform Ultimate Boundedness ◽  
Functional Differential ◽  
Image Position

SynopsisWe consider a system of functional differential equationswhere G: R × B → Rn is T periodic in t and B is a certain phase space of continuous functions that map (−∞, 0[ into Rn. The concepts of B-uniform boundedness and B-uniform ultimate boundedness are introduced, and sufficient conditions are given for the existence of a T-periodic solution to (1.1). Several examples are given to illustrate the main theorem.

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