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Sandwich Theorems for Semicontinuous Operators

Published online by Cambridge University Press:  20 November 2018

J. M. Borwein  and
M. Théra
J. M. Borwein
Affiliation:
Department of Mathematics, Statistics and Computing Science Dalhousie University Halifax, Nova Scotia B3H 3J5
M. Théra
Affiliation:
Département de Mathématiques Université de Limoges Limoges 87060, France
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Abstract

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We provide vector analogues of the classical interpolation theorems for lower semicontinuous functions due to Dowker and to Hahn and Katetov-Tong.

Résumé

Résumé

Le but de cet article est de montrer que sous certaines conditions, les théorèmes d'interposition de Dowker, Hahn et Katetov-Tong ont des analogues pour des applications à valeurs vectorielles et semi-continues inférieurement.

Keywords

54C0854C6054C6554F05Sandwich theoremsinterpolation theoremsselection theoremssemicontinuous operatorvector latticelattice-like
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 4 , 01 December 1992 , pp. 463 - 474
Copyright
Copyright © Canadian Mathematical Society 1992

References

[B-G-K-K-T] Bank, B., Guddat, J., Klatte, D., Kummer, B., Tammer, K., Nonlinear parametric optimization. Akademie Verlag, Berlin, 1982.Google Scholar
[Be] Beer, G., Lattice semicontinuous functions and their applications, Houston J. Math. 13(1987), 303–318.Google Scholar
[Ber] Berge, C., Espaces topologiques. (2nd éd.), Paris, 1966.Google Scholar
[Bo] Borwein, J. M., Continuity and differintiability properties of convex operators, Proc. London Math. Soc. 44(1982), 420–444.Google Scholar
[Bo-Pe-Th] Borwein, J. M., Penot, J-R, Théra, M., Conjugate convex operators, Journal of Math. Anal, and Appl. 102(1984), 399–414.Google Scholar
[Ce] Cellina, A., A fixed point theorem for subsets of L1, multifunctions and integrands. Catania, 1983. Lecture Notes in Math. 1091, Springer-Verlag, 1984.Google Scholar
[Du] Dugundji, J., Topology. Allyn and Bacon, Inc., Boston, 1970.Google Scholar
[E] Engleking, R., General Topology. Polish Scientific Publishers, Warsaw, 1977.Google Scholar
[Ho] Holmes, R. B., Geometric functional analysis and its applications. Springer-Verlag, 1975.Google Scholar
[Ja] Jameson, G. J. O., Topology and normed spaces. Chipman and Hall, London, 1974.Google Scholar
[Ku] Kuratowski, K., Topology I. PWN-Academic Press, 1966.Google Scholar
[Lee-Spa] Lechicki, A., Spakowski, A., A note on intersection of lower semicontinuous multifunctions, Proc. Amer. Math. Soc. (1) 95(1986), 114–122.Google Scholar
[L-P] Luchetti, R., Patrone, F., Closure and upper semicontinuity results in mathematical programming, Nash and economic equilibria, Optimization 17(1980), 619–628.Google Scholar
[Lux-Za] W. Luxemburg, A. J., Zaanen, A. C., Riesz Spaces, Vol. 1, North-Holland, 1971.Google Scholar
[No] Noll, D., Continuous affine support mappings for convex operators, J. of Func. Anal., (2)76(1988), 411– 431.Google Scholar
[Pe-Th] Penot, J-P., Théra, M., Semicontinuous mappings in general topology, Ark. Mat. (2)38(1982), 158–166.Google Scholar
[Ro] Robert, R., Convergence de fonctionnelles convexes, C.R. Acad. Sci. Paris 278(1973), 905–907.Google Scholar
[Sch﹜] Schaeffer, H. H., Halbgeordnete lokalkonvex Vectorrame, 111, Math. Ann. 141(1960), 113–142.Google Scholar
[SCI12] Schaeffer, H. H., Topological vector spaces. Springer-Verlag, 1970.Google Scholar
[Spa] Spakowski, A., On approximation by step multifunctions, Comment. Math. (2)28(1985), 363–371.Google Scholar
[Str] Stromberg, K. R., Introduction to classical real analysis. Wardsworth International Mathematics Series.Google Scholar
[Th] Théra, M., Étude des fonctions convexes vectorielles semi-continues. Thèse, Université de Pau, 1978.Google Scholar
[Van Go] van Gool, F., Semicontinuousfunctions with values in a uniform ordered space. Preprint 559, University of Utrecht, 1989.Google Scholar
[Yo] Yosida, K., Functional analysis. Springer-Verlag, New York, 1978.Google Scholar