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凸函数的几个Hadamard型不等式
Several Inequalities of Hadamard′s Type for Convex Functions
【摘要】 对于凸函数建立了几个新的 Hadamard型不等式 ,比如f ∑nk=1qkak∫A+yA- yg(x) dx ∫A+yA- yf (x) g(x) dx ∑nk=1qkf (ak) ∫A+yA- yg(x) dx和f (pa +qb) p∫ξaf (x) g(x) dx∫ξag(x) dx+q∫bξf (x) g(x) dx∫bξg(x) dx pf (a) +qf (b)等 ,推广了前人所做的工作 .
【Abstract】 We establish several new inequalities of Hadamard′s type for convex functions, f∑nk1q ka k∫ A+y A-yg(x)dx∫ A+y A-yf(x)g(x)dx∑nk1q kf(a k)∫ A+y A-yg(x)dxandf(pa+qb)p∫ξ af(x)g(x)dx∫ξ ag(x)dx+q∫b ξf(x)g(x)dx∫b ξg(x)dxpf(a)+qf(b)etc, which generalize works doine by the predecessor.
【关键词】 凸函数;
Hadamard不等式;
可积函数;
【Key words】 convex function, Hadamard′s inequalities; integrable function;
【Key words】 convex function, Hadamard′s inequalities; integrable function;
- 【文献出处】 数学的实践与认识 ,Mathematics In Practice and Theory , 编辑部邮箱 ,2005年01期
- 【分类号】O174
- 【被引频次】4
- 【下载频次】192