Abstract
The purpose of this paper is to show stability of order preserving/ reversing transforms on the class of non-negative convex functions in \({\mathbb{R}}^{n}\), and its subclass, the class of non-negative convex functions attaining 0 at the origin (these are called “geometric convex functions”). We show that transforms that satisfy conditions which are weaker than order preserving transforms, are essentially close to the order preserving transforms on the mentioned structures.
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Acknowledgements
The authors would like to express their sincere appreciation to Prof. Vitali Milman and Prof. Shiri Artstein-Avidan for their support, advice and discussions. Dan Florentin was Partially supported by the Israel Science Foundation Grant 865/07. Alexander Segal was Partially supported by the Israel Science Foundation Grant 387/09.
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© 2012 Springer-Verlag Berlin Heidelberg
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Florentin, D., Segal, A. (2012). Stability of Order Preserving Transforms. In: Klartag, B., Mendelson, S., Milman, V. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2050. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29849-3_12
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DOI: https://doi.org/10.1007/978-3-642-29849-3_12
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