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The Dual \(\phi \)-Brunn–Minkowski Inequality

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Abstract

In this paper, we define a dual \(\phi \)-combination \({\widetilde{Q}}_{\phi , \xi }\). Using the log-convexity of strictly decreasing convex function \(\phi ^{-1}\), we give the dual \(\phi \)-Brunn–Minkowski inequality. Moreover, the equivalence between the dual \(\phi \)-Brunn–Minkowski inequality and the dual \(\phi \)-Minkowski mixed volume inequality is demonstrated.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Qinghai Normal University, Xining, 810000, China

    Wei Shi & Tian Li

  2. Department of Mathematics, China Three Gorges University, Yichang, 443002, China

    Weidong Wang

  3. Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, China

    Weidong Wang

Authors
  1. Wei Shi
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  2. Tian Li
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  3. Weidong Wang
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Correspondence to Tian Li.

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Research is supported by the Natural Science Foundation of China (Grant No.11371224), the Research Foundation of Qinghai Normal University (Grant No.2019zr002), and the Research Foundation of Qinghai Normal University (Grant No.2020QZR009).

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Shi, W., Li, T. & Wang, W. The Dual \(\phi \)-Brunn–Minkowski Inequality. Mediterr. J. Math. 18, 195 (2021). https://doi.org/10.1007/s00009-021-01834-1

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  • DOI: https://doi.org/10.1007/s00009-021-01834-1

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