凸集上投影算子的一个单调性质

本文证明了投影算子的一个新的单调性质，并简要讨论了与其它单调性质的关系     

包含函数Γ（x）的对数完全单调函数及不等式

基于欧拉Gamma函数的奇特性质,利用函数的单调性理论以及一些简单函数的积分表达式与级数展开式证明了函数f_α(x),α∈R和函数s(x)的对数完全单调性,并利用该性质得出了一个比原有结论更精确的不等式以及一个双边不等式.     

函数单词性的应用

学过函数的性质后,觉得单调性是函数的所有性质中,最为一般的一种性质．因为几乎所有的函数都有单调性可言,并且在解决诸如确定函数的单调区间、求函数值域、最大（小）值等数学问题时,可大显身手．有些表面上与函数的单调性关联不大数学问题,     

一些特殊函数的完全单调性

欧拉Gamma函数是一种非常重要的函数,在数学的许多分支以及物理、工程等学科中都有着十分重要的作用.而完全单调性以及对数完全单调性是Gamma函数的重要性质.主要证明了一些包含Gamma函数和Psi函数在内的特殊函数的完全单调性和对数完全单调性,并由此推出了一些重要的不等式.     

聚焦指数函数单调性的应用

单调性是函数的重要性质之一,而指数函数的单调性更是尤为重要.对于指数函数y=a^x(a>0,a≠1),当a>1时,它在实数集R上单调递增;当a∈(0,1)时,它在实数集R上单调递减.由此可见,指数函数的单调性并不复杂,但它的应用却不简单,它可以用来比较大小、求函数的定义域、求函数的最值或值域、求参数的值或范围、解方程或证明不等式,还可以解决综合性问题.     

判断函数单调性的三种策略

函数的重要性质之一就是单调性,函数的单调性应用广泛,利用函数单调性对解决某些数学问题也有“奇效”,故而函数单调性也一直是高考数学的热门考点,常作为解题中至关重要的一个环节出现.如何判断函数的单调性也是很多学生面临的问题,故本文结合具体例题来介绍三种常见的解题思路：利用函数单调性的定义判断、利用导数判断、利用“同增异减”规律判断.     

导数在研究函数单调性中的应用

函数的单凋性是函数的重要性质，若利用定义求解，变形的技巧和方法是阻碍问题解决的难点，而利用导数研究单调性问题，可有效地突破这个难点，利用导数的相关知识来研究函数的单调性已成为高考的热点．     

如何用导数判断函数单调性

函数的单调性是函数的重要性质,也是高考的热点问题,若利用函数定义求解,一般较为复杂．但是利用导数求函数的单调就有效地解决了这一难题．     

巧用函数单调性解题

函数单调性是函数的一个重要性质，它刻画出函数图形局部升降趋势．利用函数的单调性可求解一些较复杂的问题，下面仅就三个方面以例说明．     

Orlicz-Sobolev空间单调性及其在最佳逼近中的应用

改进了Hudzik,Kurc关于最佳逼近中的结果,给出了赋Orlicz范数的Orlicz- Sobolev空间具有一致单调性、局部一致单调性和严格单调性的充要条件、单调系数的数值,以及在最佳逼近中的应用.     

Monotonicity and best approximation in Orlicz-Sobolev spaces with the Luxemburg norm

Criteria for strict monotonicity, upper (lower) locally uniform monotonicity and uniform monotonicity of Orlicz-Sobolev spaces with the Luxemburg norm are given. Some applications to best approximation are presented.     

Complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions

We present some complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions. This extends some known results due to S.-L. Qiu and M. Vuorinen.     

Monotonicity and Consistency in Matching Markets

Objective: To obtain axiomatic characterizations of the core of one-to-one and one-to-many matching markets. Methods: The axioms recently applied to characterize the core of assignment games were adapted to the models of this paper. Results: The core of one-to-one matching markets is characterized by two different lists of axioms. The first one consists of weak unanimity, population monotonicity, and Maskin monotonicity. The second consists of weak unanimity, population monotonicity, and consistency. If we allow for weak preferences, the core is characterized by weak unanimity, population monotonicity, Maskin monotonicity, and consistency. For one-to-many matchings, the same lists as for the case of strict preferences characterize the core. Conclusions: The cores of the discrete matching markets are characterized by axioms that almost overlap with the axioms characterizing the core of the continuous matching markets. This provides an axiomatic explanation for the observations in the literature that almost parallel properties are obtained for the core of the two models. We observe that Maskin monotonicity is closely related to consistency in matching marketsThis research is financially supported by Waseda University Grant for Special Research Projects #2000A−887, 21COE-GLOPE, and Grant-in-Aid for Scientific Research #15530125, JSPS. This paper was presented at the 7th. International Meeting of the Society for Social Choice and Welfare held in Osaka, Japan. The comments of the participants are gratefully acknowledged. The author thanks Professors William Thomson, Eiichi Miyagawa and anonymous referees for their valuable comments and suggestions. Any remaining errors are independent     

Points of monotonicity in Orlicz-Lorentz function spaces

In Orlicz-Lorentz function space ?_M,ω[0,γ), points of upper monotonicity, lower monotonicity, upper local uniform monotonicity (γ<∞) and lower local uniform monotonicity (γ<∞) are characterized. As the corollary, we can easily obtain the criteria for strict monotonicity, upper local uniform monotonicity (γ<∞) and lower local uniform monotonicity (γ<∞) of ?_M,ω[0,γ).     

赋Luxemburg范数的Musielak-Orlicz-Sobolev空间单调性在最佳逼近中的应用

借鉴Orlicz-Sobolev空间的单调性在最佳逼近中一些应用,利用Musielak-Orlicz-Sobolev空间的构成特点,给出了赋Luxemburg范数的Musielak-Orlicz-Sobolev空间的单调性在最佳逼近中一些应用的充分性定理.     

A remark on the Brézis–Browder theorem in finite dimensional spaces

Brézis and Browder gave an important characterization of maximal monotonicity for linear operators, in reflexive Banach spaces. In this paper, we show that this characterization also preserves the maximal p-monotonicity, in finite dimensional spaces.     

两个Abel积分的比值单调性的判别条件

用直接计算的方法对文献中给出的第三类函数的一种特殊形式给出其积分比值单调性的判别条件.