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  • Research Article
  • Open Access

Comparing the relative volume with the relative inradius and the relative width

Journal of Inequalities and Applications20062006:54542

https://doi.org/10.1155/JIA/2006/54542

  • Received: 28 February 2006
  • Accepted: 29 August 2006
  • Published:

Abstract

We consider subdivisions of a convex body in two subsets and . We obtain several inequalities comparing the relative volume: (1) with the minimum relative inradius, (2) with the maximum relative inradius, (3) with the minimum relative width, and (4) with the maximum relative width. In each case, we obtain the best upper and lower estimates for subdivisions determined by general hypersurfaces and by hyperplanes.

Keywords

  • Relative Volume
  • Convex Body
  • Lower Estimate
  • Relative Width
  • General Hypersurface

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Authors’ Affiliations

(1)
Departamento de Análisis Matemático, Universidad de Alicante, Campus de San Vicente del Raspeig, Alicante, 03080, Spain

References

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Copyright

© A. Cerdán 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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