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A Volume Product Representation and Its Ramifications in lnp, 1≤p≤∞

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DOI: 10.4236/apm.2011.15046    2,750 Downloads   5,833 Views   Citations

ABSTRACT

Let|Bnp|,1<p<∞ , be the volume of the unit p-ball in Rn and q the Hölder conjugate exponent of p. We represent the volume product |Bnp| |Bna| as a function free of its gamma symbolism. This representation will allows us in this particular case to confirm, using basic classical analysis tools, two conjectured and partially proved lower and upper bounds for the volume product of centrally symmetric convex bodies of the Euclidean Rn . These bounds in the general case play a central role in convex geometric analysis.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

D. Karayannakis, "A Volume Product Representation and Its Ramifications in lnp, 1≤p≤∞," Advances in Pure Mathematics, Vol. 1 No. 5, 2011, pp. 264-266. doi: 10.4236/apm.2011.15046.

References

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[3] D. Karayannakis, “An algorithm for the Evaluation of the Gamma function and Ramifications. Part I,” International Journal of Mathematics, Game Theory and Algebra, Vol. 19, No. 4, 2010.
[4] L. E. Lutwak, “Selected Affine Isoperimetric Inequalities, Handbook of Convex Geometry,” North-Holland Publishing Co., Amsterdam, 1993.

  
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