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1.
In this paper, we introduce an iteration process of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for an inverse strongly-monotone mapping, and then obtain a weak convergence theorem. Using this result, we obtain a weak convergence theorem for a pair of a nonexpansive mapping and a strictly pseudocontractive mapping. Further, we consider the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse strongly-monotone mapping. 相似文献
2.
§1. IntroductionSiddiqiandAnsari[4]developediterativealgorithmsforfindingapproximatesolutiontonewclassesofquasivariationalinequalitiesinHilbertspaces,HassouniandMoudafi[1]extendthemainideasofpaper[4]tomoregeneralcases,whichconsideredaclassofvariation… 相似文献
3.
该文的目的是通过研究一个一般的迭代过程, 来寻求一族非扩张映射的不动点集与强单调映射的变差不等式解集的公共元素. 相似文献
4.
In this paper, we prove strong convergence of Mann iterative schemes to fixed points of multi-valued demicontractive non-self mappings in complete CAT(0) spaces under appropriate conditions. In addition, △? convergence or strong convergence of Mann iterative scheme to a fixed point of single-valued k-strictly pseudocontractive non-self mapping is obtained. Our theorems improve and unify most of the results in the literature. 相似文献
5.
The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically
strict pseudocontractive mapping in the intermediate sense and the set of solutions of the variational inequality problem
for a monotone, Lipschitz continuous mapping. We introduce a modified hybrid Mann iterative scheme with perturbed mapping
which is based on well-known CQ method, Mann iteration method and hybrid (or outer approximation) method. We establish a strong
convergence theorem for three sequences generated by this modified hybrid Mann iterative scheme with perturbed mapping. Utilizing
this theorem, we also design an iterative process for finding a common fixed point of two mappings, one of which is an asymptotically
strict pseudocontractive mapping in the intermediate sense and the other taken from the more general class of Lipschitz pseudocontractive
mappings. 相似文献
6.
主要研究了带误差的非扩张映象及强伪压缩映象的Ishikawa迭代序列的收敛性问题,推广了已知的相关结果。 相似文献
7.
In this paper, we introduce two iterative sequences for finding a common element of the set of fixed points of a nonexpansive
mapping and the set of solutions of an equilibrium problem in a Hilbert space. Then, we show that one of the sequences converges
strongly and the other converges weakly. 相似文献
8.
9.
Viscosity approximation methods for generalized equilibrium problems and fixed point problems 总被引:1,自引:0,他引:1
The purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a generalized
equilibrium problem (for short, GEP) and the set of fixed points of a nonexpansive mapping in the setting of Hilbert spaces.
By using well-known Fan-KKM lemma, we derive the existence and uniqueness of a solution of the auxiliary problem for GEP.
On account of this result and Nadler’s theorem, we propose an iterative scheme by the viscosity approximation method for finding
a common element of the set of solutions of GEP and the set of fixed points of a nonexpansive mapping. Furthermore, it is
proven that the sequences generated by this iterative scheme converge strongly to a common element of the set of solutions
of GEP and the set of fixed points of a nonexpansive mapping. 相似文献
10.
利用粘性逼近方法,在自反Banach空间的框架下,研究无限族非扩张映象及对给定的压缩映象的迭代程序的收敛性问题.在适当的条件下,证明了该迭代序列强收敛于某一公共不动点,而且这一公共不动点也是自反Banach空间中某一变分不等式的唯一解.所得结果改进和推广了一些人的最新的结果. 相似文献
11.
周泽民 《数学年刊A辑(中文版)》2011,32(4):481-488
证明了如果f~μ是单位圆△上塌陷型极值拟共形映射,则存在与f~μ等价的极值拟共形映射f~(?)以及单位圆的子区域G,使得面(z)=0,(?)z∈G. 相似文献
12.
In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then we show that the sequence converges weakly to a common element of two sets. 相似文献
13.
朱剑峰 《数学年刊A辑(中文版)》2018,39(1):33-42
设w(z)为单位圆盘U到约当区域Ω?C上的调和映照.给出w(z)具有Lipschitz性质的等价条件.进一步地,若Ω为有界凸区域,对其边界函数给出一个较弱的条件,使得w=P[f](z)为调和拟共形映照. 相似文献
14.
J. W. Peng 《Journal of Optimization Theory and Applications》2010,144(1):107-119
In this paper, we introduce some iterative algorithms for finding a common element of the set of solutions of a mixed equilibrium
problem, the set of fixed points of a strict pseudocontraction and the set of solutions of a variational inequality for a
monotone, Lipschitz continuous mapping. We obtain both weak and strong convergence theorems for the sequences generated by
these processes in Hilbert spaces. 相似文献
15.
§1. IntroductionIn1933,H.Cartan[1]suggestedthatthegeometricalfunctiontheorybeextendedtoseveralvariables.However,hepointedoutthattheGrowthandKoebe1/4-Theoremaregenerallynottrueforbiholomorphicmappings,sohesuggestedthestudyofstarlikemappingsandconvexm… 相似文献
16.
In this paper, we introduce and study a new class of general strongly nonlinear quasivariational inequalities and construct a general iterative algorithm by using the projection method. We establish the existence of a unique solution for general strongly nonlinear quasivariational inequalities involving relaxed Lipschitz, relaxed monotone, and strongly monotone mappings; we obtain the convergence and stability of the iterative sequences generated by the algorithm. Our results extend, improve, and unify many known results due to Bose, Noor, Siddiqi-Ansari, Verma, Yao, Zeng, and others. 相似文献
17.
This paper analyses the properties of the projection mapping over a set defined by a constraint function whose image is possibly
a nonpolyhedral convex set. Under some nondegeneracy assumptions, we prove the (strong) semismoothness of the projection mapping.
In particular, we derive the strong semismoothness of the projection mapping when the nonpolyhedral convex set under consideration
is taken to be the second-order cone or the semidefinite cone. We also derive the semismoothness of the solution to the Moreau–Yosida
regularization of the maximum eigenvalue function. 相似文献
18.
Hemant Kumar Pathak 《Numerical Functional Analysis & Optimization》2018,39(4):449-466
A new 𝒮-generated Ishikawa iteration with errors is proposed for a pair of quasi-nonexpansive mapping and uniformly L-Lipschitzian asymptotically pseudo-contractive mapping in real Banach spaces. We show that the proposed iterative scheme converges strongly to a common solution of quasi-nonexpansive mapping and uniformly L-Lipschitzian asymptotically pseudo-contractive mapping in real Banach spaces. A comparison table is prepared using a numeric example which shows that the proposed iterative algorithm is faster than some known iterative algorithms. 相似文献
19.
§ 1. Introduction Anecessaryandsufficientconditionandasufficientconditiontoensurethataset valuedmappingandasingle valuedmappinginacompletemetricspaceandacompleteconvexmetricspacehavingacommonfixedpointarerespectivelygivenin [1 ] .Meanwhilethemainresultsin[2 ]— [5]areimprovedandextendedin [1 ] .Inthispaper ,theexistenceatcommonfixedpointsoftwoset valuedmappingandasing valuedmappingwerestudied ,andthecorrespond ingresultsin [1 ]— [5]wereextendedandimproved .Let(X ,d)beanon emptymetricspa… 相似文献