共查询到18条相似文献,搜索用时 78 毫秒
1.
关于p-凸函数的Hadamard型不等式 总被引:2,自引:0,他引:2
对于P-凸函数在给定连续区间上的算术平均问题,通过P-凸函数理论将其转化为定积分问题,利用定积分的定义计算和定积分运算,建立了P-凸函数的Hadamard 型不等式,给出了证明和发现不等式的实例. 相似文献
2.
宋振云 《纯粹数学与应用数学》2012,(1):36-40
基于P-凸函数的函数凸性,研究了P-凸函数的Jensen型不等式的积分形式,通过定积分的定义计算,得到了P-凸函数的积分型Jensen不等式;利用P-凸函数的一个充要条件,建立了P-凸函数的积分型Jensen不等式的加权形式. 相似文献
3.
由凸函数的充要条件,证明关于凸函数的三个命题,据以讨论凸函数的几何特征,给出凸函数的三种分类以及其对应图形,由此得出关于凸函数的几个结论. 相似文献
4.
5.
可微凸函数的又一特征 总被引:4,自引:0,他引:4
设函数,f(x)在区间Ⅰ内二阶可导。文[1,P.175]、[2]指出以下命题互相等价: (ⅰ) f(x)为Ⅰ上的上(下)凸函数; (ⅱ) f″(x)≤(≥)0(x∈Ⅰ); (ⅲ) f(x)+f(y)≤(≥)2f(x+y/2)(x,y∈Ⅰ); 本文获得了凸函数的又一特征: 相似文献
6.
本文提出了两类新的广义凸函数—强预拟不变凸函数与强拟不变凸函数.讨论了强预拟不变凸函数与强拟不变凸函数间的关系,强拟不变凸函数与强伪不变凸函数间的关系.研究了强预拟不变凸函数在多目标优化中的应用. 相似文献
7.
8.
9.
10.
11.
In this paper, we establish a decomposition theorem for polyharmonic functions and consider its applications to some Dirichlet problems in the unit disc. By the decomposition, we get the unique solution of the Dirichlet problem for polyharmonic functions (PHD problem) and give a unified expression for a class of kernel functions associated with the solution in the case of the unit disc introduced by Begehr, Du and Wang. In addition, we also discuss some quasi-Dirichlet problems for homogeneous mixed-partial differential equations of higher order. It is worthy to note that the decomposition theorem in the present paper is a natural extension of the Goursat decomposition theorem for biharmonic functions. 相似文献
12.
Chuanyi Zhang 《Czechoslovak Mathematical Journal》1997,47(3):385-394
Vector-valued pseudo almost periodic functions are defined and their properties are investigated. The vector-valued functions contain many known functions as special cases. A unique decomposition theorem is given to show that a vector-valued pseudo almost periodic function is a sum of an almost periodic function and an ergodic perturbation. 相似文献
13.
A new class of generalized convex set-valued functions, termed nearly-subconvexlike functions, is introduced. This class is a generalization of cone-subconvexlike maps, nearly-convexlike set-valued functions, and preinvex set-valued functions. Properties for the nearly-subconvexlike functions are derived and a theorem of the alternative is proved. A Lagrangian multiplier theorem is established and two scalarization theorems are obtained for vector optimization. 相似文献
14.
Enrique Jordá 《Journal of Mathematical Analysis and Applications》2007,327(1):739-743
In this brief note, we extend Vitali's theorem for holomorphic functions obtained by Arendt and Nikolski to nets of functions of sheaves of smooth vector-valued functions. As a consequence we also extend a Harnack's theorem for compact operator-valued harmonic functions recently obtained by Enflo and Smithies to bounded operator-valued harmonic functions, avoiding the assumption that the Hilbert space H where the operators are defined is separable. 相似文献
15.
L. Kuntz 《Journal of Optimization Theory and Applications》1995,86(1):263-270
A new implicit function theorem for a class of nonsmooth functions is proved. It is used to improve the directional implicit function theorem of Demidova and Demyanov (Ref. 1). 相似文献
16.
In this paper, we define finitely additive, probability and modular functions over semiring-like structures. We investigate finitely additive functions with the help of complemented elements of a semiring. We also generalize some classical results in probability theory such as the law of total probability, Bayes’ theorem, the equality of parallel systems, and Poincaré’s inclusion-exclusion theorem. While we prove that modular functions over a couple of known semirings are almost constant, we show it is possible to define many different modular functions over some semirings such as bottleneck algebras and the semiring (Id(D),+,?), where D is a Dedekind domain. 相似文献
17.
《Journal of the Egyptian Mathematical Society》2014,22(1):14-18
This paper is motivated by an open problem of Luke’s theorem. We consider the problem of developing a unified point of view on the theory of inequalities of Humbert functions and of their general ratios are obtained. Some particular cases and refinements are given. Finally, we obtain some important results involving inequalities of Bessel and Whittaker’s functions as applications. 相似文献
18.
On duality theory in multiobjective programming 总被引:5,自引:0,他引:5
D. T. Luc 《Journal of Optimization Theory and Applications》1984,43(4):557-582
In this paper, we study different vector-valued Lagrangian functions and we develop a duality theory based upon these functions for nonlinear multiobjective programming problems. The saddle-point theorem and the duality theorem are derived for these problems under appropriate convexity assumptions. We also give some relationships between multiobjective optimizations and scalarized problems. A duality theory obtained by using the concept of vector-valued conjugate functions is discussed.The author is grateful to the reviewer for many valuable comments and helpful suggestions. 相似文献