星体的Green-Osher型不等式及其应用OA
Green-Osher Type Inequality for Star Bodies and Its Applications
为比较星体P和Q对偶相对Steiner多项式根的范数平方‖(t)k‖2以及相对径向函数(φ)k的大小,通过第j阶对偶相对Steiner多项式的根定义一个非负的实数r0,类比平面凸体Green-Osher不等式的证明方法,推导出Rn 中星体的Green-Osher型不等式.基于此结果,得到两个对偶Minkowski型不等式.
To compare the squared norm ‖(t)k‖2 of the dual relative Steiner polynomial roots with the relative radial function (φ)k for star bodies P and Q,a nonnegative real num-ber r0 was defined by the roots of the j-th dual relative Steiner polynomial.Then analo-gously to the method of proving Green-Osher inequality for planar convex bodies,a Green-Osher type inequality for star bodies in Rn was deduced.Based on this result,two dual Minkowski type inequalities were obtained.
丁洁;张德燕;袁名扬
淮北师范大学数学与统计学院,淮北 235000淮北师范大学数学与统计学院,淮北 235000淮北师范大学数学与统计学院,淮北 235000
数理科学
星体Steiner多项式Green-Osher不等式Minkowski不等式
star bodySteiner polynomialGreen-Osher inequalityMinkowski inequality
《青岛大学学报（自然科学版）》 2025 (3)
1-6,6
安徽省高校自然科学研究重大项目(批准号:2022AH040067)资助安徽省高等学校省级质量工程项目(批准号:2022kcsz256,2021jyxm1326)资助安徽省新时代育人质量工程项目课程思政示范课(批准号:2023szsfkc077)资助.
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