凸函数的延拓

利用凸函数定义的一个推广形式可统一各种特殊凸函数的定义.给出了广义凸函数的判别方法及其琴生型不等式.     

利用非可导性条件判别函数的凸性

本文先给出凸函数两个常用定义,并对连续函数证明其等价性.然后给出函数凸性的一些几何判别法和积分判别法.最后给出一个有用的微分判别法.     

半严格不变凸函数

文章在Banach空间中定义了一种新的广义凸函数—半严格不变凸函数.对于满足局部Lipschitz条件的半严格不变凸函数,得到了它的广义Clarke次微分性质.文中还讨论了半严格不变凸函数与不变凸函数及半严格预不变凸函数之间的关系,得到了半严格不变凸函数的一些性质.     

半严格不变凸函数

文章在Banach空间中定义了一种新的广义凸函数—半严格不变凸函数.对于满足局部Lipschitz条件的半严格不变凸函数,得到了它的广义Clarke次微分性质.文中还讨论了半严格不变凸函数与不变凸函数及半严格预不变凸函数之间的关系,得到了半严格不变凸函数的一些性质.     

半严格-G-E-半预不变凸型函数及其在数学规划中的应用研究

提出了一类新的广义凸函数——半严格-G-E-半预不变凸函数,它是一类非常重要的广义凸函数,为半严格-G-半预不变凸函数与半严格-E-预不变凸函数的推广.首先给出例子,以说明半严格-G-E-半预不变凸函数的存在性及其与其他相关广义凸函数间的关系.然后讨论了半严格-G-E-半预不变凸函数的一些基本性质.最后,探究了半严格-G-E-半预不变凸型函数分别在无约束和有约束非线性规划问题中的重要应用,获得一系列最优性结论,并举例验证了所得结果的正确性.     

凸函数与半连续函数的关系

通过研究凸函数与半连续函数的关系,给出了凸函数的一个与上半连续性相结合的等价定义.     

E-凸函数的若干特征

讨论了一类广义的凸集和凸函数:E-凸集和E-凸函数的若干性质,并给出E-凸函数的一个判别准则．     

论双变量同构凸函数

在定义加权同构平均值的基础上将凸函数、几何凸函数、平方凸函数等理论统一为双变量同构凸函数理论,给出其统一的微分判别法则,并由此推导出不同类型的同构平均值间不等关系的简单判定法则.     

一类非光滑多目标半无限规划的最优性条件

利用K-方向导数,给出了一类存在性更为广泛的广义凸函数.即广义一致K-（F,α,ρ,d）-I型凸函数,进而讨论了涉及这些新广义凸性的一类多目标半无限规划的最优性条件。     

连续凸函数的判据及几何特征

从凸函数定义出发研究了连续函数与凸函数的关系,给出了连续凸函数的几个判定条件,并刻划它们的几何特征.     

半模糊凸模糊映射

In this paper, a new class of fuzzy mappings called semistrictly convex fuzzy mappings is introduced and we present some properties of this kind of fuzzy mappings. In particular, we prove that a local minimum of a semistrictly convex fuzzy mapping is also a global minimum. We also discuss the relations among convexity, strict convexity and semistrict convexity of fuzzy mapping, and give several sufficient conditions for convexity and semistrict convexity.     

一类对称函数的Schur-几何凸性Schur-调和凸性

讨论一类对称函数的Schur-几何凸性和Schur-调和凸性.作为应用,利用控制理论,也得到一些新的分析不等式.     

On convexity of a planar domain with a pair of concave tomography projections

We describe simple sufficient conditions on tomography-type measurements of a planar set which imply convexity of this set. The cases of partial convexity and higher-dimensional sets are considered as well.     

Support-type properties of generalized convex functions

Chebyshev systems induce in a natural way a concept of convexity. The functions convex in this sense behave in many aspects similarly to ordinary convex functions. In this paper support-type properties are investigated. Using osculatory interpolation, the existence of support-like functions is established for functions convex with respect to Chebyshev systems. Unique supports are determined. A characterization of the generalized convexity via support properties is presented.     

Locally uniform convexity in Musielak-Orlicz function spaces of Bochner type endowed with the Luxemburg norm

Criteria for locally uniform convexity of Musielak-Orlicz function spaces of Bochner type equipped with the Luxemburg norm are given. We also prove that, in Musielak-Orlicz function spaces generated by locally uniformly convex Banach space, locally uniform convexity and strict convexity are equivalent.     

解析函数的p叶性条件

本文指出 Ｍ．Ｊａｈａｎｇｉｒｉ的评论［Ｍａｔｈｅｍａｔｉｃａｌ Ｒｅｖｉｅｗｓ　９８ｅ：３００２０］错误，并且导出解析函数ｐ叶星形性与ｐ叶凸性的某些充分条件．     

Abstract convexity of extended real-valued ICR functions

The theory of non-negative increasing and co-radiant (ICR) functions defined on ordered topological vector spaces has been well developed. In this article, we present the theory of extended real-valued ICR functions defined on an ordered topological vector space X. We first give a characterization for non-positive ICR functions and examine abstract convexity of this class of functions. We also investigate polar function and subdifferential of these functions. Finally, we characterize abstract convexity, support set and subdifferential of extended real-valued ICR functions.     

Optimality Conditions in Differentiable Multiobjective Programming

In this paper, three sufficient conditions are given, one of which modifies the previous result given by Singh (Ref. 1) under the assumption of convexity of the functions involved at the Pareto-optimal solution. A counterexample has been furnished which shows that the convexity assumption cannot be extended to include the quasiconvexity case. The second theorem on sufficiency requires the strict pseudoconvexity of the functions involved.     

Optimality and duality with generalized convexity

Hanson and Mond have given sets of necessary and sufficient conditions for optimality and duality in constrained optimization by introducing classes of generalized convex functions, called type I and type II functions. Recently, Bector defined univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, optimality and duality results for several mathematical programs are obtained combining the concepts of type I and univex functions. Examples of functions satisfying these conditions are given.     

Generalized monotonicity and convexity of non-differentiable functions

The relationships between (strict, strong) convexity of non-differentiable functions and (strict, strong) monotonicity of set-valued mappings, and (strict, strong, sharp) pseudo convexity of non-differentiable functions and (strict, strong) pseudo monotonicity of set-valued mappings, as well as quasi convexity of non-differentiable functions and quasi monotonicity of set-valued mappings are studied in this paper. In addition, the relations between generalized convexity of non-differentiable functions and generalized co-coerciveness of set-valued mappings are also analyzed.