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On the Reverse Orlicz Blaschke–Santal\(\acute{\mathrm{o}}\) Inequality

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Abstract

In this paper, the Orlicz centroid body defined by Lutwak, Yang and Zhang and the extrema of some affine invariant functionals involving the volume of the Orlicz centroid body are investigated. The reverse form of the Orlicz Blaschke–Santal\(\acute{\mathrm{o}}\) inequalities is obtained for two-dimensional convex sets.

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Acknowledgements

We would like to thank the referees for valuable suggestions and comments that lead to improvement of the original manuscript. In addition, we would like to thank Dr. Weichi Wu for his helpful help.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Hexi University, Zhangye, Gansu, 734000, People’s Republic of China

    Tongyi Ma

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  1. Tongyi Ma
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Correspondence to Tongyi Ma.

Additional information

This work is supported by the National Natural Science Foundations of China (Grant Nos.11561020, 11161019) and is partly supported by the National Natural Science Foundations of China (Grant No. 11371224). E-mail: matongyi@126.com (Tongyi Ma).

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Ma, T. On the Reverse Orlicz Blaschke–Santal\(\acute{\mathrm{o}}\) Inequality. Mediterr. J. Math. 15, 32 (2018). https://doi.org/10.1007/s00009-018-1081-4

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  • DOI: https://doi.org/10.1007/s00009-018-1081-4

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