Abstract
An inequality of K. Mahler, together with its case of equality, due to M. Meyer, are extended to integrals of powers of polar-conjugate concave functions. An application to estimation of the volume-product of certain convex bodies is given.
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References
Alzer H (1992) On an integral inequality for concave functions. Acta Sci Math56: 79–82
Mahler K (1939) Ein Minimalproblem für konvexe Polygone. Mathematica (Zutphen)B7: 118–127
Meyer M (1991) Convex bodies with minimal volume product in ℝ2. Mh Math112: 297–301
Meyer M, Pajor A (1990) On the Blaschke-Santaló inequality, Arch Math55: 82–93
Petty CM (1985) Affine isoperimetric problems. In:Goodman JE, Lutwak E, Malkevitch J, Pollack R (eds) Discrete Geometry and Convexity. Ann New York Acad Sci440: 113–127
Santaló LA (1949) Un invariante afin para los cuerpos convexos del espacio de n dimensiones. Portugaliae Math8: 155–161
Schneider R (1993) Convex Bodies: The Brunn-Minkowski Theory, Cambridge: University Press
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Meyer, M., Reisner, S. Inequalities involving integrals of polar-conjugate concave functions. Monatshefte für Mathematik 125, 219–227 (1998). https://doi.org/10.1007/BF01317315
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DOI: https://doi.org/10.1007/BF01317315