共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, the concept of c-compact mapping is introduced. A generalization of Browder’s fixed point theorem and some equivalence forms are given. As applications, the existence of solutions for some variational inequalities and monotone operator equations is discussed. 相似文献
2.
Satit Saejung 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(10):3431-3439
We prove strong convergence theorems for a sequence which is generated by Halpern’s iteration. We also apply our result for finding zeros of an accretive operator. Our result improves the recent result of Aoyama et al. [K. Aoyama, Y. Kimura, W. Takahashi, M. Toyoda, Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space, Nonlinear Anal. 67 (2007) 2350-2360] by removing some assumptions on the parameters. Finally we discuss the new sufficient condition studied by Song [Y. Song, A new sufficient condition for the strong convergence of Halpern type iterations. Appl. Math. Comput. 198 (2) (2008) 721-728; Y. Song, New strong convergence theorems for nonexpansive nonself-mappings without boundary conditions. Comput. Math. Appl. 56 (6) (2008) 1473-1478] and correct the main result of Song and Chai [Y. Song, X. Chai, Halpern iteration for firmly type nonexpansive mappings, Nonlinear Anal. 71 (10) (2009) 4500-4506]. 相似文献
3.
A. Amini-Harandi 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(12):4661-4665
In this paper, we first prove some generalizations of Caristi’s fixed point theorem. Then we give some applications to the fixed point theory of weakly contractive set-valued maps and the minimization problem. 相似文献
4.
S. Dhompongsa A. Kaewkhao B. Panyanak 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(2):459-468
We prove a strong convergence theorem for multivalued nonexpansive mappings which includes Kirk’s convergence theorem on CAT(0) spaces. The theorem properly contains a result of Jung for Hilbert spaces. We then apply the result to approximate a common fixed point of a countable family of single-valued nonexpansive mappings and a compact valued nonexpansive mapping. 相似文献
5.
Zhilong Li 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(12):3751-3755
Without assumptions on the continuity and the subadditivity of η, by means of Caristi’s fixed point theorem, we investigated the existence of fixed points for a Caristi type mapping which partially answered Kirk’s problem and improved Caristi’s fixed point theorem, Jachymski’s fixed point theorem and Khamsi’s fixed point theorem since φ is not necessarily assumed to be bounded below on X. 相似文献
6.
Shahram Saeidi 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):546-548
In this note, we deal with an iterative scheme of Halpern type for a semigroup of nonexpansive mappings on a compact convex subset of a strictly convex and smooth Banach space with respect to an asymptotically left invariant sequence of means defined on an appropriate space of bounded real valued functions of the semigroup. We improve the corresponding result of [A.T. Lau, H. Miyake, W. Takahashi, Approximation of fixed points for amenable semigroups of nonexpansive mappings in Banach spaces, Nonlinear Anal. 67 (2007) 1211-1225]. 相似文献
7.
In-Sook Kim 《Topology and its Applications》2007,154(17):3056-3069
Some ways to obtain upper and lower bounds for measures of noncompactness of retractions onto spheres in infinite-dimensional normed spaces are discussed. Moreover, relations with 0-epi maps are revealed and the extension of condensing maps on spheres is discussed. As an application, some results of Birkhoff-Kellog type and Nussbaum's fixed point theorem on spheres are obtained. 相似文献
8.
Recently Proinov [P.D. Proinov, A generalization of the Banach contraction principle with high order of convergence of successive approximations, Nonlinear Analysis (2006), doi:10.1016/j.na.2006.09.008] generalized Banach contraction principle with high order of convergence. We extend some results of Proinov to the case of multi-valued maps from a complete metric space X into the space of all nonempty proximinal closed subsets of X. Our results not only generalize Nadler’s fixed-point theorem (in the case when T is a mapping from a complete metric space X into the space of all nonempty proximinal closed subsets of X) but also gives high order of convergence. As an application, we obtain an existence theorem for first-order initial value problem. 相似文献
9.
The main result of this paper is that a closed convex subset of a Banach space has the fixed point property for nonexpansive mappings if and only if it has the fixed point property for nonexpansive semigroups. 相似文献
10.
Lu-Chuan Ceng Jen-Chih Yao 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(12):3742-3750
Assume that X is a real Banach space with uniformly normal structure and C is a nonempty closed convex subset of X. We show that a κ-uniformly Lipschitzian semigroup of nonlinear self-mappings of C admits a common fixed point if the semigroup has a bounded orbit and if κ is appropriately greater than one. This result applies, in particular, to the framework of uniformly convex Banach spaces. 相似文献
11.
We study the strong convergence of two viscosity iteration processes for pseudo-contractive semigroup and for ?-strongly pseudo-contractive mapping in uniformly convex Banach spaces with uniformly Gâteaux differentiable norm. As special cases, we get strong convergence of two viscosity iteration processes for approximating common fixed points of nonexpansive semigroups in certain Banach spaces. The results presented in this paper extend and generalize previous results. 相似文献
12.
The purpose of this paper is to study the strong convergence of a process of implicit iteration to a common fixed point for a finite family of asymptotically hemi-contractive mappings. Our results extend a recent result of M.O. Osilike and B.G. Akuchu [Common fixed points of a finite family of asymptotically pseudocontractive maps, Fixed Point Theory Appl. 2 (2004) 81–88] from Hilbert spaces to p-uniformly convex Banach spaces with p>1. 相似文献
13.
SONGWEN 《高校应用数学学报(英文版)》1995,10(4):463-466
This paper proposes a formally stronger set-valued Claxke‘s fixed point theorem. By this-theorem we can improve a fixed point theorem for weakly inward contraction set-valued mapping of D. Dowing and W.A. Kirk. 相似文献
14.
Amro Alsheikh Ali 《Quaestiones Mathematicae》2016,39(3):319-340
In this paper, we establish some new nonlinear Leray-Schauder alternatives for the sum and the product of weakly sequentially continuous operators in Banach algebras satisfying certain sequential condition (P). The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. As an application, our results are used to prove the existence of solutions for a nonlinear integral equation. 相似文献
15.
We study the approximation of common fixed points of a finite family of nonexpansive mappings and suggest a modification of the iterative algorithm without the assumption of any type of commutativity. Also we show that the convergence of the proposed algorithm can be proved under some types of control conditions. 相似文献
16.
We prove two nonlinear ergodic theorems for noncommutative semigroups of nonexpansive mappings in Banach spaces. Using these
results, we obtain some nonlinear ergodic theorems for discrete and one-parameter semigroups of nonexpansive mappings.
Dedicated to Professors Albrecht Dold and Ed Fadell 相似文献
17.
In [C.O. Chidume, G. De Souza, Convergence of a Halpern-type iteration algorithm for a class of pseudocontractive mappings, Nonlinear Analysis (2007), doi:10.1016/j.na.2007.08.008], the authors proved a strong convergence result for strictly pseudo-contractive mappings using a Halpern-type iteration algorithm. However, the main result is not correct. In this note, we provide a counter-example to the theorem. 相似文献
18.
In this note, we will modify several gaps in Chidume and Ofoedu [C.E. Chidume, E.U. Ofoedu, A new iteration process for generalized Lipschitz pseudo-contractive and generalized Lipschitz accretive mappings, Nonlinear Anal. (2006), in press (doi:10.1016/j.na.2006.05.012)]. 相似文献
19.
In this paper, we introduce a new two-step iterative scheme for two asymptotically nonexpansive nonself-mappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for the new two-step iterative scheme in a uniformly convex Banach space. 相似文献
20.
Moosa Gabeleh 《Quaestiones Mathematicae》2016,39(2):203-215
A new class of noncyclic mappings, called generalized noncyclic relatively nonexpansive, is introduced and used to study the existence of best proximity pairs in the setting of uniformly convex Banach spaces. We also obtain a weak convergence theorem for noncyclic relatively nonexpansive mappings in the setting of Hilbert spaces. 相似文献