Orlicz Version of Mixed Mean Dual Affifine Quermassintegrals

C. -J. Zhao () and W. -S. Cheung ()
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C. -J. Zhao: China Jiliang University, Department of Mathematics
W. -S. Cheung: The University of Hong Kong, Department of Mathematics

A chapter in Approximation Theory and Analytic Inequalities, 2021, pp 509-527 from Springer

Abstract: Abstract In this paper, our main aim is to generalize the mixed mean dual affine quermassintegrals to the Orlicz space. Under the framework of Orlicz dual Brunn–Minkowski theory, we introduce a new geometric operator by calculating the first Orlicz variation of the mixed mean dual affine quermassintegrals and call it the Orlicz mixed mean dual affine quermassintegrals. The fundamental notions and conclusions of the mixed mean dual affine quermassintegrals, and the Minkowski and Brunn–Minkowski inequalities for the mixed mean dual affine quermassintegrals are extended to an Orlicz setting, and the related concepts and inequalities of Orlicz dual quermassintegrals are also included in our conclusions. The new Orlicz isoperimetric inequalities in special case yield the Orlicz dual Minkowski inequality and Orlicz dual Brunn–Minkowski inequality, which also imply the L p-dual Minkowski inequality and Brunn–Minkowski inequality for the mixed mean dual affine quermassintegrals.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-60622-0_25

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DOI: 10.1007/978-3-030-60622-0_25

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