scholarly journals Korovkin sets for an operator on a space of continuous functions

1976 ◽  
Vol 65 (2) ◽  
pp. 337-345 ◽  
Author(s):  
Le Baron Ferguson ◽  
Michael D. Rusk
Keyword(s):  
Continuous Functions ◽  
Space Of Continuous Functions

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.

Cone-Monotone Functions: Differentiability and Continuity

2005 ◽  
Vol 57 (5) ◽  
pp. 961-982 ◽  
Author(s):  
Jonathan M. Borwein ◽  
Xianfu Wang
Keyword(s):  
Banach Spaces ◽  
Convex Cone ◽  
Continuous Functions ◽  
Monotone Functions ◽  
Empty Interior ◽  
Space Of Continuous Functions

AbstractWe provide a porosity-based approach to the differentiability and continuity of real-valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone K with non-empty interior. We also show that the set of nowhere K-monotone functions has a σ-porous complement in the space of continuous functions endowed with the uniform metric.

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