共查询到20条相似文献,搜索用时 31 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.
Banach空间中严格渐近伪压缩映象的收敛性问题 总被引:1,自引:0,他引:1
胡良根 《应用泛函分析学报》2005,7(3):228-233
在一致凸的Banach空间中,采用新的证明方法研究了严格渐近伪压缩映象和渐近非膨胀映象带误差的修正的Mann和Ishikawa迭代程序的收敛性问题,不要求定义域、值域有界,且迭代系数更简单. 相似文献
3.
在Banach空间中,利用锥理论和单调迭代方法研究了一类非线性算子方程的解和最小最大耦合解的存在与迭代逼近定理,并应用到Banach空间中非线性Volterra型积分方程和常微分方程的初值问题. 相似文献
4.
Yekini Shehu 《Optimization》2018,67(4):475-492
The purpose of this paper is to present an accelerated hybrid viscosity and steepest-descent method for solving proximal split feasibility problems (if solutions exist) in real Hilbert spaces. We obtain strong convergence of the sequence generated by our scheme under some suitable conditions on the parameters. In all our results in this work, our iterative schemes are proposed with a way of selecting the step sizes such that their implementation does not need any prior information about the bounded linear operator norm. Finally, we give numerical comparisons of our results with other established result to verify the efficiency and implementation of our new method. 相似文献
5.
Ke Ding Nan-Jing Huang Jong Kyu Kim 《Journal of Applied Mathematics and Computing》2006,21(1-2):379-391
In this paper, we introduce and study a new system of generalized nonlinear co-complementarity problems with set-valued mappings and construct an iterative algorithm for approximating the solutions of the system of generalized co-complementarity problems. We prove the existence of the solutions for the system of generalized co-complementarity problems with set-valued mappings without compactness and the convergence of iterative sequences generated by the algorithm in Hilbert spaces. We also study a new perturbed iterative algorithm for approximating a system of generalized co-complementarity problems with single-valued mappings in Hilbert spaces. 相似文献
6.
In this paper, we introduce two iterative schemes for approximating solutions of generalized variational inequalities in the setting of Banach spaces. The existence of solutions of this general problem and the convergence of the proposed iterative schemes to a solution are established. 相似文献
7.
Zeqing Liu Haijiang Dong Shin Min Kang Sunhong Lee 《Journal of Optimization Theory and Applications》2013,157(3):696-715
This paper is concerned with a new functional equation arising in dynamic programming of multistage decision processes. Utilizing the Banach fixed point theorem and iterative algorithms, we prove the existence, uniqueness, and iterative approximations of solutions for the functional equation in Banach spaces and a complete metric space, respectively. Some error estimates between the iterative sequences generated by iterative algorithms and the solutions are discussed. Five examples are constructed to illustrate the results presented in this paper. 相似文献
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The Stokes semigroup on a bounded domain is an analytic semigroup on spaces of bounded functions as was recently shown by the authors based on an a priori L ∞-estimate for solutions to the linear Stokes equations. In this paper, we extend our approach to exterior domains and prove that the Stokes semigroup is uniquely extendable to an analytic semigroup on spaces of bounded functions. 相似文献
10.
Jianghua Fan 《Journal of Mathematical Analysis and Applications》2008,337(2):1041-1047
In this paper, we study the existence of solutions and approximation of the solutions by using a Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces. The results presented in this paper generalize the corresponding results of J. Li [J. Li, On the existence of solutions of variational inequalities in Banach spaces, J. Math. Anal. Appl. 295 (2004) 115-126]. 相似文献
11.
研究了Banach空间中拟-似变分包含解的存在与逼近问题.给出了一种寻求解的新的迭代算法,建立了具混合误差的Ishikawa型迭代序列强收敛到解的充要条件.所得结果推广了一些相关的结果. 相似文献
12.
In this paper, we propose an iterative method of approximating solutions for a class of the system of generalized variational inequalities and give a convergence result for the iterative method in uniformly convex and uniformly smooth Banach spaces. 相似文献
13.
Ge DONG 《数学年刊B辑(英文版)》2021,42(3):333-356
In this paper, the author studies the existence of the minimal nonnegative solutions of some elliptic variational inequalities in Orlicz-Sobolev spaces on bounded or unbounded domains. She gets some comparison results between different solutions as tools to pass to the limit in the problems and to show the existence of the minimal solutions of the variational inequalities on bounded domains or unbounded domains. In both cases,coercive and noncoercive operators are handled. The sufficient and necessary conditions for the existence of the minimal nonnegative solution of the noncoercive variational inequality on bounded domains are established. 相似文献
14.
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
15.
In this paper, we introduce new random iterative sequences with errors approximating a unique random common fixed point for three random set-valued strongly pseudo-contractive mappings and show the convergence of the random iterative sequences with errors by using an approximation method in real uniformly smooth separable Banach spaces. As applications, we study the existence of random solutions for some kind of random nonlinear operator equations group in separable Hilbert spaces. 相似文献
16.
L. P. Castro S. Saitoh Y. Sawano A. M. Sim?es 《Complex Analysis and Operator Theory》2012,6(1):307-324
In this paper we shall introduce new constructions of approximate solutions of general linear partial differential equations
with constant coefficients on the whole spaces, and establish fundamental estimates of the solutions depending on the inhomogeneous
terms. This will be done by combining general ideas of the Tikhonov regularization and discretization of bounded linear operator
equations on reproducing kernel Hilbert spaces. Furthermore, we will provide approximate solutions for the related inverse
source problems. 相似文献
17.
COMPARISON, SYMMETRY AND MONOTONICITY RESULTS FOR SOME DEGENERATE ELLIPTIC OPERATORS IN CARNOT-CARATHEODORY SPACES
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This paper studies the properties of solutions of quasilinear equations involving the p-laplacian type operator in general Carnot-Caratheodory spaces.The authors show some com-parison results for solutions of the relevant differential inequalities and use them to get somesymmetry and monotonicity properties of solutions,in bounded or unbounded domains. 相似文献
18.
In this paper, we introduce a composite explicit viscosity iteration method of fixed point solutions of variational inequalities for nonexpansive semigroups in Hilbert spaces. We prove strong convergence theorems of the composite iterative schemes which solve some variational inequalities under some appropriate conditions. Our result extends and improves those announced by Li et al [General iterative methods for a one-parameter nonexpansive semigroup in Hilbert spaces, Nonlinear Anal. 70 (2009) 3065–3071], Plubtieng and Punpaeng [S. Plubtieng, R. Punpaeng, Fixed-point solutions of variational inequalities for nonexpansive semigroups in Hilbert spaces, Math. Comput. Modelling 48 (2008) 279–286], Plubtieng and Wangkeeree [S. Plubtieng, R. Wangkeeree, A general viscosity approximation method of fixed point solutions of variational inequalities for nonexpansive semigroups in Hilbert spaces, Bull. Korean Math. Soc. 45 (4) (2008) 717–728] and many others. 相似文献
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In this paper,we consider a nonlinear neutral differential equation.By the Schauder fixed point theorem,some sufficient conditions are obtained to ensure the existence of uncountably many bounded positive solutions.In addition,we give the iterative approximation sequences with errors for these positive solutions and establish some error estimates between the approximate and the positive solutions. 相似文献