共查询到20条相似文献,搜索用时 234 毫秒
1.
Zeqing Liu Haijiang Dong Sun Young Cho Shin Min Kang 《Journal of Optimization Theory and Applications》2013,157(3):716-736
This paper deals with a functional equation and inequality arising in dynamic programming of multistage decision processes. Using several fixed-point theorems due to Krasnoselskii, Boyd–Wong and Liu, we prove the existence and/or uniqueness and iterative approximations of solutions, bounded solutions and bounded continuous solutions for the functional equation in two Banach spaces and a complete metric space, respectively. Utilizing the monotone iterative method, we establish the existence and iterative approximations of solutions and nonpositive solutions for the functional inequality in a complete metric space. Six examples which dwell upon the importance of our results are also included. 相似文献
2.
Zeqing Liu Jingjing Zhu Shin Min Kang Jeong Sheok Ume 《Journal of Global Optimization》2013,57(3):969-995
This paper studies the existence, uniqueness and iterative approximations of solutions, bounded solutions and continuous bounded solutions for a functional equation arising in dynamic programming of multistage decision processes by using fixed point theorems and the iterative methods in complete metric spaces and Banach spaces, respectively. Four examples are given to illustrate the validity and applications of the results presented in this paper. 相似文献
3.
介绍了集值映象的伪单调定义,并在Banach空间中构造了集值混和变分不等式问题近似解的迭代算法.应用伪单调映象定义,证明了该迭代算法收敛于集值混和变分不等式问题的近似解.特别值得注意的是:在文章中对集值映象没有Lipschitz连续性假设. 相似文献
4.
The purpose of this paper is to introduce a new system of generalized resolvent equations with corresponding system of variational
inclusions in uniformly smooth Banach spaces. We establish an equivalence relation between system of generalized resolvent
equations and system of variational inclusions. The iterative algorithms for finding the approximate solutions of system of
generalized resolvent equations are proposed. The convergence of approximate solutions of system of generalized resolvent
equations obtained by the proposed iterative algorithm is also studied.
相似文献
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Banach空间中二阶积分-微分方程的初值问题 总被引:5,自引:0,他引:5
王文霞 《应用泛函分析学报》2003,5(2):132-142
使用锥理论及单调迭代技术,首先讨论了Banach空间中一阶积分-微分方程初值问题的最小最大解的存在性,并在此基础上讨论了带有一阶微分项的二阶积分-微分方程初值问题的最小最大解的存在性。 相似文献
7.
In this paper, we propose three different kinds of iteration schemes to compute the approximate solutions of variational inequalities in the setting of Banach spaces. First, we suggest Mann-type steepest-descent iterative algorithm, which is based on two well-known methods: Mann iterative method and steepest-descent method. Second, we introduce modified hybrid steepest-descent iterative algorithm. Third, we propose modified hybrid steepest-descent iterative algorithm by using the resolvent operator. For the first two cases, we prove the convergence of sequences generated by the proposed algorithms to a solution of a variational inequality in the setting of Banach spaces. For the third case, we prove the convergence of the iterative sequence generated by the proposed algorithm to a zero of an operator, which is also a solution of a variational inequality. 相似文献
8.
研究了Banach空间中非线性混合型微分-积分方程初值问题u′=f(t,u,Tu,Su),u(0)=x0的整体解,完全没有要求f的任何增性,利用Mnch不动点定理和比较结果得到了初值问题整体解的存在性和唯一解,并且给出了一致收敛于唯一解的迭代序列,改进推广和统一了已有的许多结果. 相似文献
9.
BOUNDARY VALUE PROBLEM FOR NONLINEAR IMPULSIVE INTEGRO-DIFFERENTIAL EQUATION IN BANACH SPACE 总被引:1,自引:0,他引:1
In this paper, by establishing a new comparison result and using the monotone iterative technique, the existence of maximal and minimal solutions of the boundary value problem for second-order impulsive differential equation which depends on x' in Banach space is obtained. 相似文献
10.
Monotone iterative technique for neutral fractional differential equation with infinite delay 下载免费PDF全文
Renu Chaudhary Dwijendra N. Pandey 《Mathematical Methods in the Applied Sciences》2016,39(15):4642-4653
In this paper, we employ the method of lower and upper solutions coupled with the monotone iterative technique to obtain existence and uniqueness of extremal mild solutions to neutral fractional differential equation with infinite delay in an ordered Banach space. The results are obtained by using the theory of fractional calculus, monotone iterative technique, measure of noncompactness, and semigroup theory. Finally, we discuss an example to illustrate our results. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
11.
In this paper,we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-strongly monotone operator and the set of common fixed points of two infinite families of relatively nonexpansive mappings or the set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings in Banach spaces.Then we study the weak convergence of the two iterative sequences.Our results improve and extend the results announced by many others. 相似文献
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一类非线性算子方程解的存在唯一性定理及其应用 总被引:4,自引:1,他引:3
在抽象连续函数空间中,用迭代方法讨论了一类非线性算子方程解的存在唯一性,并将其结果应用于Banach空间中的积分方程. 相似文献
13.
Banach空间中一类广义混合非线性隐拟变分包含解的三步迭代 总被引:3,自引:0,他引:3
本文引入并研究了实Banach空间中一类新的广义混合非线性隐拟变分包含 ,通过对实Banach空间中的m 增生映象运用Nadler定理和Michael选择定理 ,构建了这类新的广义变分包含解的三步迭代算法 ,并证明了其解的存在性和由迭代算法生成的迭代序列的收敛性 相似文献
14.
The purpose of this paper is to study some iterative algorithms for finding a common element of the set of solutions of systems of variational inequalities for inverse-strongly accretive mappings and the set of fixed points of an asymptotically nonexpansive mapping in uniformly convex and 2-uniformly smooth Banach space or uniformly convex and q-uniformly smooth Banach space. Strong convergence theorems are obtained under suitable conditions. We also give some numerical examples to support our main results. The results obtained in this paper improve and extend the recent ones announced by many others in the literature. 相似文献
15.
Bin Zhou Zhao-Yan Li Guang-Ren Duan Yong Wang 《Journal of Computational and Applied Mathematics》2009
This paper is concerned with weighted least squares solutions to general coupled Sylvester matrix equations. Gradient based iterative algorithms are proposed to solve this problem. This type of iterative algorithm includes a wide class of iterative algorithms, and two special cases of them are studied in detail in this paper. Necessary and sufficient conditions guaranteeing the convergence of the proposed algorithms are presented. Sufficient conditions that are easy to compute are also given. The optimal step sizes such that the convergence rates of the algorithms, which are properly defined in this paper, are maximized and established. Several special cases of the weighted least squares problem, such as a least squares solution to the coupled Sylvester matrix equations problem, solutions to the general coupled Sylvester matrix equations problem, and a weighted least squares solution to the linear matrix equation problem are simultaneously solved. Several numerical examples are given to illustrate the effectiveness of the proposed algorithms. 相似文献
16.
《Communications in Nonlinear Science & Numerical Simulation》2010,15(10):2809-2817
In this paper, we study the existence of solutions of a nonlinear functional integral equation of fractional order with deviating arguments. This equation is considered in the Banach space of real functions defined, continuous and bounded on an unbounded interval. Moreover, we show that solutions of this integral equation are locally attractive. An example is provided to illustrate the theory. 相似文献
17.
In this paper we prove the existence of mild solutions for neutral functional integrodifferential equation in a Banach space.
The results are obtained by using the Schaefer fixed-point theorem. 相似文献
18.
该文利用单调迭代技术讨论了Banach空间中含有非线性一阶微分项x'的二阶脉冲积分-微分方程初值问题的最大最小解的存在性问题. 作为该文主要结论的应用,作者给出了一个例子. 相似文献
19.
Jiao-Xun Kuang 《计算数学(英文版)》1990,8(4):333-341
There are several methods for solving operator equations in a Banach space. The successive approximation methods require the spectral radius of the iterative operator be less that 1 for convergence. In this paper, we try to use the incomplete semiiterative methods to solve a linear operator equation in Banach space. Usually the special semiiterative methods are convergent even when the spectral radius of the iterative operator of an operator of an operator equation is greater than 1. 相似文献
20.
A new class of bilevel generalized mixed equilibrium problems involving set-valued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued mappings are suggested and analyzed. Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions. The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed. These results are new and generalize some recent results in this field. 相似文献