Szasz型算子同时逼近的点态结果

本文给出了Ｓｚａｓｚ－ｉｒａｋｊａｎ算子和Ｓｚａｓｚ－Ｋａｎｔｏｒｏｖｉｃｈ算子组合的同时逼近的点态结果，并用其导数给出了高阶Ｌｉｐｓｃｈｉｔｚ函数类的特征刻划。     

非线性多值算子扰动的映射定理

本文讨论非线性多值算子的非紧扰动的映射定理,并给出非线性泛函方程ｚ∈Ｔ（ｘ）＋Ｆ（ｘ）可解性的最新结果,其中Ｔ是多值算子且（Ｔ＋１/ｎＩ）^－１是１－集压缩,而Ｆ是１－集压缩或γ－凝聚．所得的结果改善了［５,８,１２］中的主要结果     

一类Bernstein-Durrmeyer算子线性组合算子的Lp逼近

讨论了Ｂｅｒｎｓｔｅｉｎ－Ｄｕｒｒｍｅｙｅｒ算子的一类线性组合算子的Ｌｐ逼近,给出了正定理、逆定理及逼近阶的特征刻划。     

一类EPD算子乘积与抛物算子乘积Cauchy问题解的结构关系

1.引言 J.Hadamard首先研究了双曲方程与抛物方程基本解之间的关系,[3]建立了非抛物型方程Hadamard基本解的展开式系数升维洁构,并利用这种升维结构改进了[1]的结果;[5]解决了一类空间维数任意的双曲方程基本解、Cauchy问题解的极限问题。以     

一类修正的Szasz—Kantorvich算子与Baskakov—Kantorovich算子的逼近定理

该文利用三对角无穷方阵修正Ｓｚａｓｚ－Ｋａｎｔｏｒｖｉｃｈ（以下简记Ｓ－Ｋ）算子与Ｂａｓｋａｋｏｖ－Ｋａｎｔｏｒｏｖｉｃｈ（以下简记Ｂ－Ｋ）算子。对于这两类修正的算子，我们得到了Ｈ．Ｈｅｒｅｎｓ和Ｇ．Ｇ．Ｌｏｒｅｅｎｔｚ型的结果以及在Ｌｐ（０）中逼近的正逆定理。     

扭化的Atiyah-Singer算子(Ⅱ)

本文证明了从Ｄｏｌｂｅａｕｌｔ算子可以得出一个扭化的Ａｔｉｙａｈ－Ｓｉｎｇｅｒ算子,它与原来的算子具有相同的主象征．特别地,辛流形上的Ｄｏｌｂｅａｕｌｔ算子是一个扭化的Ａｔｉｙａｈ－Ｓｉｎｇｅｒ算子．     

J—自共轭微分算子谱的定性分析

本文对J－自共轭微分算子谱理论研究情况做一些概要性的介绍,第一部分简要回顾了J－自共轭微分算子理论研究的发展过程,第二,三部分介绍了J－自共轭微分算子的本质谱和离散谱定性分析的主要方法和结论;第四部分扼要叙述J－自共轭微分算子其它方面的一些工作,以及J－自共轭微分算子谱理论研究中尚待解决的问题。     

K—单调算子方法及应用

本文讨论了稠定的K-单调非线性算子的扩张,在较弱的条件下得到K-单调算子方程广义解的存在性、唯一性和投影法近似可解性的结果,最后应用于不可压缩的粘性流体绕流平板的边界层计算问题,数值效果良好。     

Hamacher算子的一个新性质及其应用

完善了Hamacher算子的定义;发现了Hamacher算子的一个新性质;分析了Hamacher算子与其它模糊算子之间的关系。最后,根据Hamacher算子的新性质,给出了一个新的模糊评判的方法。     

Fuzzy带算子环和Fuzzy带算理想

提出Fuzzy带算子环、Fuzzy带算理想和Fuzzy带算商环的定义,讨论它们的一些初等性质。     

Positive Definite Solutions of Operator Equations X m + A * X - n A = I

In this article, we discuss the positive definite solutions of the operator equation X m + A * X -n A = I , , on a Hilbert space. Necessary and sufficient conditions for the existence of a positive semi-definite solution are derived. Under some conditions, two effective iterative methods for getting a positive definite solution of this equation are proposed and error estimations are obtained.     

Positive Definite Solutions of Operator Equations X m + A * X − n A = I

In this article, we discuss the positive definite solutions of the operator equation X m + A * X m n A = I , , on a Hilbert space. Necessary and sufficient conditions for the existence of a positive semi-definite solution are derived. Under some conditions, two effective iterative methods for getting a positive definite solution of this equation are proposed and error estimations are obtained.     

Remarks on the Notion of Order of Difference Equations

In the paper, the notion of order of a difference equation is introduced in such a way that this order is invariant with respect to the change of the independent variable. For the general case, a formula for the general solution of linear difference equation of k -th order is given. It is shown that, in contrast to differential equations, the dimension of the linear space of solutions of linear homogenous difference equation can be lowered if their domain of definition is restricted appropriately.     

Convex operators: some subdifferentiability results

The subdifferentiability properties of convex operators are intimately related to the properties of the ordered (topological) vector spaces they range in. This relation is investigated for various types of subdifferentiability notions     

Lipschitzian Operators of Substitution in the Algebra ΛBV

We present necessary and sufficient conditions on the generating functions of operators of substitution (=Nemytskii superposition operators), which map the Waterman space v BV of functions of v -bounded variation on the interval into another space of this type and satisfy the Lipschitz condition.     

A new t-norm

We define a new t-norm, and t-conorm, whose domain is usually a restricted subset of [0, 1] x [0, 1], with one parameter, the correlation coefficient between the membership values, which ranges from −1 to 1. We then investigate their properties showing at one extreme they equal the Zadeh operators (max, min), and at the other extreme they produce the Lukasiewicz operators (max(a + b - l, 0), min(a + b,1)).     

Weak estimates cannot be obtained by extrapolation

We give a short elementary proof of the fact that weak-type estimates cannot be obtained via extrapolation.