关于局部极小值点为整体极小值点的函数的一点注记

本引进了一种广义严格拟凸函数的定义,给出了它的一个刻画,证明 了局部极小值点为整体极小值点的函数与本定义的广义严格拟凸函数的等价性。     

拟凸函数可行方向的一些结论

求文根据文［１］的启示，作者给出了可行方向的定义，＃证了拟凸函数可行方向的一些结论，亦给出了超拟凸函数可行方向的刻画，这些结论在研讨目标函数或约束函数具拟凸类函数的规划问题的最优性条件时是有用的．     

拟凸函数和Hadamard不等式

建立了若干关于拟凸函数的新的Hadamard型不等式,所得结果包含了某些文献中的结果作为我们不等式的特例.     

拟凸函数与切比晓夫逼近

木文第一节给出拟凸函数和显拟凸函数(explicitly quasiconvex functions)的一个新的特征;同时引进一种新的凸性——我们称它为强伪凸性,并给出它的若干重要性质.第二节讨论第一节的结果在最佳一致逼近中的应用,建立了交错定理、唯一性定理和强唯一性定理.     

s-orliz拟凸函数的一些性质

我们给出了定义在线性空间中的s-orliz凸集上的s-orliz拟凸函数,并讨论了其部分性质.     

二阶可微广义凸函数的性质

本对二阶可微拟凸函数、曲凸函数、严格曲凸函数进行了讨论，给出了它们的一些性质。     

拟凸函数的近似次微分及其在多目标优化问题中的应用

针对拟凸函数提出一类新的近似次微分,研究其性质,并将近似次微分应用到拟凸多目标优化问题近似解的刻画中.首先,对已有的近似次微分进行改进,得到拟凸函数新的近似次微分,并给出其与已有次微分之间的关系及一系列性质.随后,利用新的近似次微分给出拟凸多目标优化问题近似有效解、近似真有效解的最优性条件.     

某些一致倒结构的亚纯多叶函数类的系数估计

利用从属关系定义了某些新的一致倒结构的星象,凸象,近于凸和拟凸函数类,并得到了相应函数类的系数估计.其结果改进并推广了一些已有结论.     

一类广义弧式凸函数的局部极小与整体极小的关系

1 引言凸函数有一重要性质,即局部极小必为整体极小．在对凸函数所做的各种推广中,关于局部极小与整体极小的关系问题讨论甚多．本文引进了一种新的广义凸函数,即所谓的弧式严格局部拟凸函数,并证明了一个定义在Rn中紧弧式连通集M上的连续函数．若其每个局部极小均为整体极小,则此函数必为弧式严格局部拟凸函数．这是作者见     

算子Dα及其刻划的亚纯p叶函数类

用算子Dα刻划了亚纯星象函数,亚纯凸象函数,亚纯近于凸函数和亚纯拟凸函数的新子类,建立了包含关系,讨论了这些类中函数积分算子的性质.     

Adaptive subgradient method for the split quasi-convex feasibility problems

In this paper, we consider a type of the celebrated convex feasibility problem, named as split quasi-convex feasibility problem (SQFP). The SQFP is to find a point in a sublevel set of a quasi-convex function in one space and its image under a bounded linear operator is contained in a sublevel set of another quasi-convex function in the image space. We propose a new adaptive subgradient algorithm for solving SQFP problem. We also discuss the convergence analyses for two cases: the first case where the functions are upper semicontinuous in the setting of finite dimensional, and the second case where the functions are weakly continuous in the infinite-dimensional settings. Finally some numerical examples in order to support the convergence results are given.     

准凸映照齐次展开式的精细估计

本文给出C~n中单位多圆柱上和复Banach空间中单位球上的准凸映照(含A型准凸映照和B型准凸映照)f齐次展开式的精细估计,其中x=0是f(x)-x的k 1阶零点.同时,还讨论了复Banach空间单位球上准凸映照的构造,它为准凸映照齐次展开式的精细估计提供极值映照.     

AN INEQUALITY OF HOMOGENEOUS EXPANSION FOR BIHOLOMORPHIC QUASI-CONVEX MAPPINGS ON THE UNIT POLYDISK AND ITS APPLICATION

In this article,the authors obtain an inequality of homogeneous expansion for f,where f is a quasi-convex mapping(including quasi-convex mapping of type A and quasi-convex mapping of type B)defined on the open unit polydisk in C n .Meanwhile,the authors also investigate its application.     

Cn中拟凸映射和星形映射的系数问题

§ 1.　Introduction　　Theconvexfunctionshavebeenextensivelystudiedinonecomplexvariable .Thesefunc tionsareeasilycharacterizedbysimpleanalyticorgeometricconditionsandtherearemanywellknownresultswhichcanhelpusunderstandtheirnature.However,thedifficultiesariseinsev eralcomplexvariables.Imposingtheconditionthatamappingbeconvexmappingturnsouttobeveryrestrictiveandsothefamilyofquasi convexmappingswasintroducedbyROPERKAandSUFFRIDGETJin [1 ].In [2 ]wehaveshown :thefamilyofquasi convexmappings…     

On quasi-convex mappings of orderαin the unit ball of a complex Banach space Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In this paper, a class of biholomorphic mappings named quasi-convex mapping of order a in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings. Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space X. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order a defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively.     

Proximal Point Algorithm for Quasi-Convex Minimization Problems in Metric Spaces

In this paper, the proximal point algorithm for quasi-convex minimization problem in nonpositive curvature metric spaces is studied. We prove Δ-convergence of the generated sequence to a critical point (which is defined in the text) of an objective quasi-convex, proper and lower semicontinuous function with at least a minimum point as well as some strong convergence results to a minimum point with some additional conditions. The results extend the recent results of the proximal point algorithm in Hadamard manifolds and CAT(0) spaces.     

On growth and covering theorems of quasi-convex mappings in the unit ball of a complex banach space

A class of biholomorphic mappings named “quasi-convex mapping” is introduced in the unit ball of a complex Banach space. It is proved that this class of mappings is a proper subset of the class of starlike mappings and contains the class of convex mappings properly, and it has the same growth and covering theorems as the convex mappings. Furthermore, when the Banach space is confined to ℂⁿ, the “quasi-convex mapping” is exactly the “quasi-convex mapping of type A” introduced by K. A. Roper and T. J. Suffridge.     

On quasi-convex mappings of order α in the unit ball of a complex Banach space

In this paper, a class of biholomorphic mappings named quasi-convex mapping of order α in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings.Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space Ⅹ. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order α defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively.     

THE GROWTH THEOREM FOR QUASI-CONVEX MAPPINGS IN HILBERT SPACES

In this paper, the authors extend the definition of quasi-convex mappings and obtain the corresponding growth theorem.on the unit ball of a complex Hilbert space X.