Dual<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>-Mixed Geominimal Surface Area and Related Inequalities

Ma, Tongyi; Feng, Yu

doi:10.1155/2016/1481793

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2018

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“…Ma and Feng introduced the general concept of dual L p -mixed geominimal surface area for star bodies, and established some affine isoperimetric inequalities in [19]. On this basis, we give a definition for the dual Orlicz mixed geominimal surface area in the same way.…”

Section: Main Results and Proofsmentioning

confidence: 98%

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Dual Orlicz mixed geominimal surface area

Gao¹,

Ma²,

Guo³

2018

J. Nonlinear Sci. Appl.

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Based on the classical ideas, Zhu discussed the properties and useful theories for L p -mixed geominimal surface area; meanwhile, Ma defined dual Orlicz geominimal surface area. The previous studies provide a thought to us for the study of the dual Orlicz mixed geominimal surface. In our paper, we have done the following work: attempting to use an integral form to define the dual Orlicz mixed geominimal surface area, further studyding its related properties, and listing some inequalities including Alexandrov-Fenchel type inequality, analogous cyclic inequality, Blaschke-Santaló type inequality, and affine isoperimetric inequality in Orlicz space.

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Section: Main Results and Proofsmentioning

confidence: 98%

“…Compared with the inequality (2.3) and Ma's L p -affine isoperimetric inequality, if φ(t) = |t| p , and p 1, then they become the same as follows (see [19]):…”

Section: Notation and Preliminariesmentioning

confidence: 99%