关于有界变差函数的模糊Henstock-Stieltjes积分

定义和讨论了模糊数值函数关于实值有界变差函数的Henstock-Stieltjes积分及其性质,并得到了模糊Henstock-Stieltjes可积的充分必要条件;同时给出了模糊数值函数列关于实值有界变差函数的Henstock-Stieltjes积分以及模糊数值函数关于有界变差函数列的模糊Henstock-Stieltjes积分的收敛定理.最后,讨论了模糊Henstock-Stieltjes积分原函数的绝对连续性.     

全变差有界函数列的一致(R)可积性

给出了一致有界单调函数列一致可积性定理 ,由此得出全变差序列有界的收敛函数列的一致可积性 .说明了该结论可判断一些非一致收敛函数列的逐项积分性质 .     

模糊集合的模糊度的一种表示形式

给出了当论域是有界区间时,模糊度的表示形式的一个定理,利用这个定理可以得到用熵函数和距离函数所表示的模糊度的具体形式.     

基于分段均值有界变差条件下正弦与余弦积分的收敛性

本文介绍了分段均值有界变差函数(PMBVF)的定义,分别给出了正弦与余弦积分一致收敛性的充分必要条件.     

基于结构元的模糊值函数曲面积分

针对扩张原理在模糊值函数曲面积分中的遍历性问题,结合实际应用背景给出了模糊值函数第一型曲面积分的概念及其结构元表示.通过将二维模糊点和模糊结构元的定义推广到三维空间中,给出了模糊值函数第二型曲面积分的定义及其结构元表示.研究结果不仅丰富了模糊分析学理论,而且为具有不确定性因素的工程实践提供了方法依据.     

基于模糊距离总变差的模糊识别模型及径流预报应用

根据待识别样本的加权广义欧氏权距离,基于模糊距离总变差为最小的目标函数,提出了一种新的计算模糊聚类中心矩阵、模糊模式识别矩阵与目标权重的模糊识别模型.该模型具有较好的稳定性,径流中长期预报实例说明是可行的.     

某些正线性算子对有界变差函数的点态逼近度

1 引言 R.Bojanic在文献[1]研中究了Fourier算子对有界变差函数的点态逼近度,1983年Cheng Fuhua在他的博士论文中研究了Bernstein算子对BV函数的点态逼近度。本文将给出一般正线性算子对有界变差函数的点态逼近度。作为例子,我们给出Bernstein算子和Kantorovitch算子对有界变差函数的点态逼近度。应当指出,文献[2]     

一维连续函数的Riemann-Liouville分数阶微积分

本文主要讨论闭区间上一维连续函数的Riemann-Liouville分数阶微积分.首先,证明一维连续有界变差函数的任意阶Riemann-Liouville分数阶积分仍然是连续有界变差函数.其次,给出无界变差点的定义并构造一个含有无界变差点的一维连续无界变差函数.同时证明该无界变差函数的任意阶Riemann-Liouville分数阶积分的分形维数为1.最后,证明对于任意具有有限个无界变差点的一维连续函数,其任意阶Riemann-Liouville分数阶积分的分形维数仍然是1.文中还给出了一些例子的图像和数值结果.     

复值函数的广义复模糊积分北大核心

本文给出了非负复值函数关于模糊复测度的广义复模糊积分的几种等价形式,并讨论了由该积分表示的几种复模糊积分方程有解的充要条件.在此基础上,进一步引进了一般复值函数的广义复模糊积分的概念,给出了该积分的一些基本性质,并在一定条件下证明了单调收敛定理.     

Λ有界变差函数的一些性质

本文回答了D.Waterman于1976年提出的一个有关?有界变差函数的问题,并指出有关?有界变差函数的富里埃系数的阶可以大大改进。文中还说明关于?有界变差函数的绝对收敛条件是太苛刻了,可以建立合理的要求。     

Pointwise Behavior of Double Fourier Series of Functions of Bounded Variation

We extend some recent results of S. A. Telyakovskii on the uniform boundedness of the partial sums of Fourier series of functions of bounded variation to periodic functions of two variables, which are of bounded variation in the sense of Hardy. As corollaries, we obtain the classical Parseval formula, the convergence theorem of the series involving the sine Fourier coefficients, and a lower estimate of the best approximation by trigonometric polynomials in the metric of L in a sharpened version.     

Pointwise Behavior of Double Fourier Series of Functions of Bounded Variation

We extend some recent results of S. A. Telyakovskii on the uniform boundedness of the partial sums of Fourier series of functions of bounded variation to periodic functions of two variables, which are of bounded variation in the sense of Hardy. As corollaries, we obtain the classical Parseval formula, the convergence theorem of the series involving the sine Fourier coefficients, and a lower estimate of the best approximation by trigonometric polynomials in the metric of L in a sharpened version. This research was supported by the Hungarian National Foundation for Scientific Research under Grants TS 044 782 and T 046 192.     

Multi-Valued Mappings of Bounded Generalized Variation

We study the mappings taking real intervals into metric spaces and possessing a bounded generalized variation in the sense of Jordan--Riesz--Orlicz. We establish some embeddings of function spaces, the structure of the mappings, the jumps of the variation, and the Helly selection principle. We show that a compact-valued multi-valued mapping of bounded generalized variation with respect to the Hausdorff metric has a regular selection of bounded generalized variation. We prove the existence of selections preserving the properties of multi-valued mappings that are defined on the direct product of an interval and a topological space, have a bounded generalized variation in the first variable, and are upper semicontinuous in the second variable.     

Relaxation and Γ-convergence of quadratic forms inBV(I; ℝ n )

We study the lower semicontinuous envelope and the Γ-limit of degenerate quadratic integral functionals, on the space of the vector-valued functions of bounded variation defined on an interval, which are still quadratic integral functionals. We give an integral representation formula involving a new «relaxed» matrix and some linear contraints on the derivative measure.     

On the Convergence of Bernstein-Stancu Polynomials in the Variation Seminorm

This article studies the variation detracting property and rate of approximation of the Bernstein-Stancu polynomials in the space of functions of bounded variation with respect to the variation seminorm. Moreover, we will present Voronovskaya-type theorems for Bernstein-Stancu polynomials B_{n, α, β}f and for the first derivative of these polynomials. Finally we include some graphical examples.     

Functions with a finite number of negative squares on semigroups

We consider indefinite functions on semigroups and their relation to representations in spaces with an indefinite metric. Special attention is given to functions of finite rank, where the space of representation is of finite dimension, and to functions for which the corresponding representation consists of bounded operators in Pontrjagin spaces.The authors wish to thankMarco Thill for useful remarks.     

On Henstock integral of fuzzy-number-valued functions (I)

In this paper, we define and discuss the (FH) integral for fuzzy-number-valued functions. Using a concrete structure into which we embed the fuzzy number space E¹, several necessary and sufficient conditions of integrability for fuzzy-number-valued functions are given by means of abstract function theory.     

Extensions and traces of functions of bounded variation on metric spaces

In the setting of a metric space equipped with a doubling measure and supporting a Poincaré inequality, and based on results by Björn and Shanmugalingam (2007) [7], we show that functions of bounded variation can be extended from any bounded uniform domain to the whole space. Closely related to extensions is the concept of boundary traces, which have previously been studied by Hakkarainen et al. (2014) [17]. On spaces that satisfy a suitable locality condition for sets of finite perimeter, we establish some basic results for the traces of functions of bounded variation. Our analysis of traces also produces novel pointwise results on the behavior of functions of bounded variation in their jump sets.     

Zur Verteilung der schlichten Funktionen

The functions that are holomorphic in the unit disk and do not assume the value zero there, are considered. By means of a product representation of these functions, a metric space is formed with them. It is shown that every component of this space contains at most one bounded schlicht function.     

Conformal invariants and higher-order schwarz lemmas

We derive a generalization of the Grunsky inequalities using the Dirichlet principle. As a corollary, sharp distortion theorems for bounded univalent functions are proven for invariant differential expressions which are higher-order versions of the Schwarzian derivative. These distortion theorems can be written entirely in terms of conformai invariants depending on the derivatives of the hyperbolic metric, and can be interpreted as ’Schwarz lemmas’. In particular, sharp estimates on distortion of the derivatives of geodesic curvature of a curve under bounded univalent maps are given.