Abstract
In the paper, we generalize the well-known Bellman’s and Popoviciu’s inequalities, and get new Bellman’s and Popoviciu’s type inequalities. These new results provide new estimates on inequalities of these type. As application, we establish a Minkowski inequality, which in special case yields the well-known dual Minkowski inequality for volumes difference.
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The authors express their grateful thanks to the referee for his many excellent suggestions.
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Chang-Jian Zhao: Research is supported by National Natural Science Foundation of China (11371334, 10971205). Wing-Sum Cheung: Research is partially supported by a HKU Seed Grant for Basic Research.
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Zhao, CJ., Cheung, WS. Generalizations of Popoviciu’s and Bellman’s Inequalities. Bull Braz Math Soc, New Series 51, 417–428 (2020). https://doi.org/10.1007/s00574-019-00159-8
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DOI: https://doi.org/10.1007/s00574-019-00159-8