This is an announcement for the paper "Uniform convexity and the splitting problem for selections" by Maxim V. Balashov and Dusan Repovs.
Abstract: We continue to investigate cases when the Repov\v{s}-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces. We use the notion of Polyak of uniform convexity and modulus of uniform convexity for arbitrary convex sets (not necessary balls). We study general geometric properties of uniformly convex sets. We also obtain an affirmative solution of the splitting problem for selections of certain set-valued mappings with uniformly convex images.
Archive classification: math.GN math.FA
Mathematics Subject Classification: 54C60; 54C65; 52A07; 46A55; 52A01
Citation: J. Math. Anal. Appl. 360:1 (2009), 307-316
The source file(s), balashov+repovs2-final.tex: 49005 bytes, is(are) stored in gzipped form as 0908.1216.gz with size 15kb. The corresponding postcript file has gzipped size 91kb.
Submitted from: dusan.repovs@guest.arnes.si
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