Abstract
In the setting of Banach spaces, we obtain some necessary and/or sufficient conditions to the proximity map is upper semicontinuous with respect to a suitable topology.
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References
Aubin, J.P. and Cellina, A. (1984). Differential inclusions, Springer-Verlag, Berlin.
Beer, G. (1993) Topologies on closed and closed convex sets, MIA Kluwer Acad. Publ. Dordrecht.
Beer, G., Lechicki, A., Levi, S. and Naimpally, S.A. (1992). Distance functionals and suprema of hyperspace topologies, Ann. Mat. Pura Appl., 162, 367–381.
Beer, G. and Pai, D. (1991). The prox map, J. Math. Anal. Appl., 156, 428–443.
Daffer, P.Z. and Kaneko, H. (1982). Best approximation in metric spaces, Ann. Soc. Sci. Brux. Ser. I, 96, 17–27.
Fisher, B. (1981). Common fixed points of mappings and set valued mappings, Rostock Math. Colloq., 18, 69–77.
Marino, G. (1990). Some remarks about Fisher convergence of sets in normed spaces: Proximity and farthest mappings, 1 st Lombardo Rend. Sci. Mat. Appl. A, 124, 255–267.
Marino, G. and Pietramala, P. (1991). Convergence of sets and proximity map, 1st Lombardo Rend. Sci. Mat. Appl. A, 125, 181–190.
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© 1995 Springer Science+Business Media Dordrecht
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Marino, G., Pietramala, P. (1995). Proximity Maps: Some Continuity Results. In: Singh, S.P. (eds) Approximation Theory, Wavelets and Applications. NATO Science Series, vol 454. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8577-4_26
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DOI: https://doi.org/10.1007/978-94-015-8577-4_26
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4516-4
Online ISBN: 978-94-015-8577-4
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