The Set of Hausdorff Continuous Functions - The Largest Linear Space of Interval Functions

@article{Anguelov2006TheSO,
  title={The Set of Hausdorff Continuous Functions - The Largest Linear Space of Interval Functions},
  author={Roumen Anguelov and Svetoslav Markov and Blagovest Sendov},
  journal={Reliable Computing},
  year={2006},
  volume={12},
  pages={337-363}
}
Hausdorff continuous (H-continuous) functions are special interval-valued functions which are commonly used in practice, e.g. histograms are such functions. However, in order to avoid arithmetic operations with intervals, such functions are traditionally treated by means of corresponding semi-continuous functions, which are real-valued functions. One difficulty in using H-continuous functions is that, if we add two H-continuous functions that have interval values at same argument using point… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 24 references

Lecons sur les Fonctions Discontinues

R. Baire
Collection Borel, Paris, • 1905
View 15 Excerpts
Highly Influenced

Order Convergence Structure on C(X)

R. Anguelov, J. H. van der Walt
Quaestiones Mathematicae • 2005
View 1 Excerpt

On Quasilinear Spaces of Convex Bodies and Intervals

S. Markov
J. Comput. Appl. Math • 2004
View 2 Excerpts

On the Linear Space of Hausdorff Continuous Functions, lecture delivered at the 11th GAMM–IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics

Sendov, Bl, R. Anguelov, S. Markov
2004

Optimal Control and Viscosity Solutions of Hamilton-JacobiBellman Equations, Birkäuser

M. Bardi, I. Capuzzo-Dolcetta
Boston—Basel—Berlin, • 1997
View 2 Excerpts

A Calculus for Set-Valued Maps and Set-Valued Evolution Equations, Set-Valued Analysis

Z. Artstein
1995
View 1 Excerpt

Extended Interval Arithmetic Involving Infinite Intervals

S. Markov
Mathematica Balkanica • 1992
View 1 Excerpt

Similar Papers

Loading similar papers…