单调算子

设H是实Hilbert空间，T：H→2H为极大单调算子。

Let H be a real Hilbert space and let T : H-2H be a maximal monotone operator .

该文研究集值映象方程0∈T（z）的解的迭代逼近，其中T是极大强单调算子。

The purpose of this paper is to study the iterative approximation of solutions to the set-valued mapping equation 0 ∈ T ( z ), where T is a maximal strongly monotone operator .

含参数（H，η）-单调算子变分包含组解的灵敏性分析

Sensitivity Analysis for a New System of Parametric Variational Inclusions Involving ( H ,η) - Monotone Operator

Banach空间内涉及H-η-单调算子的集值混合拟似变分包含组

System of Set-Valued Mixed Quasi-Variational-Like Inclusions Involving H-eta-Monotone Operators in Banach Spaces

三相鞍形PWM波形数据的迭代计算法基于A-极大单调算子的三步迭代算法

Iterative Algorithm of three-phase PWM Waveforms Data in Nonsinusoidal Modulation ; Three-Step Iteration about A-maximal Monotone Framework

Hilbert空间极大单调算子零点的逼近问题

Approximated Problems of Zero for Maximal - monotone Operators in Hilbert Space

涉及单调算子的随机广义Hammerstein方程

Random Generalized Hammerstein equations involving monotone operators

序区间Descartes集上二元φ-凹混合单调算子不动点存在惟一性

Existence and Uniqueness of the Fixed Point for Two-variable Concave ( convex ) Mixed Monotone Operators on Descartes Set of Order Intervals

引进了关于H和G的强单调性概念，在Hilbert空间中研究了新的一类关于（H，η）单调算子的非线性集值算子包含。

The concept of strongly monotonicity with respect to H and G and a new kind of nonlinear set-valued operator inclusions ( NSVOI ) with ( H , η) - monotone operators are introduced in Hilbert space .

本文证明了半序Banach空间中混合单调算子的耦合不动点的若干存在性定理，并将所得结果应用到非线性方程组的求解中。

In this paper , we prove some existence theorems of coupled fixed point of mixed monotone operators in the semi-ordering Banach space , and give some applications to nonlinear equations .

对于寻找极大单调算子的零点，邻近点算法（PPA）是一种重要方法。

The proximal point algorithm ( PPA ) is an important method to find the zero points of maximal monotone operators .

第三章在可分Banach空间引入了一些新的概念，如随机单调算子，随机Mann迭代序列等等。

In Chapter 3 , we introduce some new concepts such as random monotone operators , random Mann iteration and so on in a separable real Banach space .

令E为实光滑、一致凸Banach空间，E为其对偶空间，AE×E为极大单调算子且A-10≠Φ。

Let E be a real smooth and uniformly convex Banach space with E its duality space . Let AE × E be a maximal monotone operator with A - 1 0 ≠Φ .

应用与（H，η）单调算子相关的预解算子技巧提出了一个迭代算法逼近其解，并且讨论了由此算法产生的迭代序列的收敛特征。

Using resolvent operator technique associated with an ( H , η) - monotone operator , the authors suggest a new iterative algorithm for approximating a solution to ( NSVOI ) and also discuss the convergence criteria of iterative sequences generated by the algorithm .

在本文的第二章，主要介绍了关于单调算子的概念和性质，并利用关于（H，η）-单调算子的预解算子技术，能够证明变分包含组解的存在性和唯一性。

In chapter two , we mainly introduce the definitions and properties of monotone operators . Using the resolvent operator associated with ( H , η) - monotone operators , we prove the existence and uniqueness of solutions for the new system of variational inclusions .

本文通过有限维逼近的方法讨论了一类非单调算子的变分不等方程，并在所谓的（F）条件下将锐角原理推广到变分问题之中，从而得到了很一般的解的存在性。

In the paper the finite dimensional approximation method is applied to study variational inequalities equations of pseudo-monotone operators . Under ( F ) condition , acute angle principle is generalized to variation problems , and there by the existence of solution is obtained .

本文将引入新的迭代算法，并利用Lyapunov泛函，Qr算子与广义投影算子等技巧，证明了迭代序列弱收敛于极大单调算子A的零点的结论。

A new iterative scheme is introduced which is proved to be weakly convergent to zero point of maximal monotone operator A by using the techniques of Lyapunov functional , Qr operator and generalized projection operator , etc.

利用不动点定理，分别证明了在自反Banach空间中极大单调算子值域扰动的抽象结论和在Hilbert空间中m增生映射值域的扰动结果，这些结论是对以往一些工作的推广；

By using the fixed point theorems , some abstract results on perturbations of ranges for maximal monotone operators in reflexive Banach space and for m-accretive mappings in Hilbert space which are improvement to some previous works are given .

利用含有伪单调算子的变分不等式理论，研究与椭圆型算子相关的Dirichlet边值问题，并给出了它在H1（Ω）空间中解的存在唯一性。

By using the theory of variational inequalities involving pseudomonotone operator , the existence and uniqueness of the solution of Dirichlet boundary value problem involving the elliptic operator in H ~ 1 (Ω) was studied .

在实Hilbert空间中，利用极大单调算子的性质，建立了广义集值变分包含和不动点问题间的等价性。

Using the resolvent technique , we established the equivalence between the generalized set-valued variational inclusions and the fixed point problems , and some perturbed iterative algorithms , proved that its proximate solution converge to its exact solution in real Hilbert space .

使用Leray-Schauder度理论研究了带紧扰动的极大单调算子的零点问题，获得了一些新的零点定理。

In this paper we study zero problems of maximal monotone operators with compact perturbations by applying the Leray-Schauder degree theory . We obtain some new zero theorems .

运用多值分析、单调算子理论和Schauder不动点定理讨论了一类具有多点边值条件的二阶微分包含问题。

We consider a nonlinear second-order differential inclusion with a convex-valued term and nonlinear multivalued boundary conditions . Using the Schauder fixed-point theorem and techniques from multivalued analysis and from monotone operators theories , we prove the existence of a solution .

讨论不可压缩非牛顿流体非定常流动的初边值问题，应用单调算子和Schauder不动点定理证明了解的存在唯一性与正则性。

This paper deals with the initial boundary value problem of nonsteady flow of incompressible non Newtonian fluid . Using monotone operators and Schauder ′ s fixed point theorem , we prove the existence and uniqueness and the regularity of solution .

局部凸空间中多值单调算子的隐补问题

Implicit Complementarity Problems for Multivalued Monotone Operator in Locally Convex Spaces

D&半连续映射及其对单调算子方程的应用

Demicontinuous Mapping and Its Application to the Monotone Operator Equation

一类T单调算子障碍问题的块单调迭代法

Block Monotone Iterative Methods for a Type of T-monotone Operators

强单调算子方程解的松弛型迭代法

The Slack Iteration Method for the Solution of Strongly Monotone Operator Equations

关于强单调算子方程的球形迭代法

On the Ball Iterative Method for Strongly Monotone Operator Equation

非连续混合单调算子的耦合不动点定理

Theorems for coupled fixed points of discontinuous mixed monotone operators

Φ-扩张型极大单调算子的扰动定理

Theorems of Perturbations of Φ - Expansive Maximal Monotone Operator