共查询到20条相似文献,搜索用时 78 毫秒
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与几何凹函数相关的函数的准线性研究 总被引:2,自引:0,他引:2
先介绍四个与几何凹函数定积分有关的不等式,后相应定义了四个函数,证明了它们具有某种准线性.作为应用,由此可得到这些函数的单调性,使得这四个不等式在理论上得到推广和完善,并且部分解决了一个公开问题. 相似文献
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几何凹函数的一个重要性质及其应用 总被引:4,自引:0,他引:4
设a0,定义在[a,b]上的函数f在(a,b)上是几何凹函数,将证明F(x)=∫xaf(t)dt在(a,b)也为几何凹函数,并用实例说明其应用. 相似文献
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通过研究函数的凸性、单调性及相关理论,建立了关于GA-凸函数的一些新的Hadamard型不等式,这些不等式推广了最近文献中的有关结果. 相似文献
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解决了一类与积分有关的函数的凸性问题,其中的定理都是一些已知结果的加强.作为应用,它给出了二类平均和一个与Gamma函数有关的函数的凸性. 相似文献
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讨论了两个初等对称函数的商的Schur调和凸性.作为应用,得到了两个新的分析不等式.最后提出了一个有研究价值的公开问题. 相似文献
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平均值函数列 总被引:1,自引:0,他引:1
经家麒 《数学的实践与认识》1998,(3)
本文用公理方法定义了平均值函数列.从公理定义出发,推证了平均值函数列的一系列共同性质,从而概括并推广了一些常见的平均值函数列.定理1指出了两个不同的平均值函数列的大小不会因变元的增加而改变,定理2揭示了平均值函数列与凸函数之间的内在联系,定理3则给出了多种平均值函数列的构作方法. 相似文献
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Semi-B-Preinvex Functions 总被引:1,自引:0,他引:1
In this note, a class of functions, called semi-B-preinvex function, which are a generalization of the semipreinvex functions and the B-vex functions, is introduced. Examples are given to show that there exist functions which are semi-B-preinvex functions, but are neither semipreinvex nor B-vex. A property of the semi-B-preinvex functions is obtained.Communicated by F. GiannessiThis research was partially supported by a Science Committee Project, Research Foundation of Chongqing, Grant 8409. The authors are thankful to the referees and Prof. F. Giannessi for suggestions and comments which helped to give the present form to this paper. 相似文献
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Subvexormal functions and subinvexormal functions are proposed, whose properties are shared commonly by most generalized convex functions and most generalized invex functions, respectively. A necessary and sufficient condition for a subvexormal function to be subinvexormal is given in the locally Lipschitz and regular case. Furthermore, subvex functions and subinvex functions are introduced. It is proved that the class of strictly subvex functions is equivalent to that of functions whose local minima are global and that, in the locally Lipschitz and regular case, both strongly subvex functions and strongly subinvex functions can be characterized as functions whose relatively stationary points (slight extension of stationary points) are global minima. 相似文献
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本文以泛复变函数为工具,成功地构造出多项式型空间调和函数族,通过坐标变换和正交化过程,进而又获得了球函数. 相似文献
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Characterizations and Applications of Prequasi-Invex Functions 总被引:22,自引:0,他引:22
Yang X. M. Yang X. Q. Teo K. L. 《Journal of Optimization Theory and Applications》2001,110(3):645-668
In this paper, two new types of generalized convex functions are introduced. They are called strictly prequasi-invex functions and semistrictly prequasi-invex functions. Note that prequasi-invexity does not imply semistrict prequasi-invexity. The characterization of prequasi-invex functions is established under the condition of lower semicontinuity, upper semicontinuity, and semistrict prequasi-invexity, respectively. Furthermore, the characterization of semistrictly prequasi-invex functions is also obtained under the condition of prequasi-invexity and lower semicontinuity, respectively. A similar result is also obtained for strictly prequasi-invex functions. It is worth noting that these characterizations reveal various interesting relationships among prequasi-invex, semistrictly prequasi-invex, and strictly prequasi-invex functions. Finally, prequasi-invex, semistrictly prequasi-invex, and strictly prequasi-invex functions are used in the study of optimization problems. 相似文献
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双解析函数、双调和函数和平面弹性问题 总被引:9,自引:2,他引:7
通过考虑双解析函数和双调和函数的关系,对单连通区域上平面弹性问题中只有重力体力作用的应力函数建立了唯一性和存在性结果;并对单位圆区域得到了类似于Poisson公式解的积分表示式。 相似文献
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本文给出了由解析函数的实部或虚部求该解析函数的几个定理,再以例题说明其应用。这些方法及应用,解决了复变函数中这一问题的理论与计算,而且所给方法能广泛进行推广。 相似文献
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X.Q. Yang 《Journal of Optimization Theory and Applications》2003,116(2):437-452
Gap functions play a crucial role in transforming a variational inequality problem into an optimization problem. Then, methods solving an optimization problem can be exploited for finding a solution of a variational inequality problem. It is known that the so-called prevariational inequality is closely related to some generalized convex functions, such as linear fractional functions. In this paper, gap functions for several kinds of prevariational inequalities are investigated. More specifically, prevariational inequalities, extended prevariational inequalities, and extended weak vector prevariational inequalities are considered. Furthermore, a class of gap functions for inequality constrained prevariational inequalities is investigated via a nonlinear Lagrangian. 相似文献