共查询到20条相似文献,搜索用时 15 毫秒
1.
《Quaestiones Mathematicae》2013,36(1-2):89-99
Abstract We show that the Tarski-Kantorovitch Principle for continuous maps on a partially ordered set yields some fixed point theorems for contractive maps on a uniform space. Our proofs do not depend on the Axiom of Choice. 相似文献
2.
<正> Throughout the present paper it is assumed that E is a real,locally convex,Hausdorfftopological vector space,and X(?)E a nonempty compact convex subset.A multi-valuedmapping F:X→2~E is said to be upper(lower) semicontinuous if for any open(closed) setU(?)E the set{x∈X|F(x)(?)U)is open (closed) in X;or,equivalently,for any closed(open) set V(?)E the set{X∈X|F(x)∩ V(?)(?)}is closed (open) in X.Moreover,F 相似文献
3.
Zoran D. Mitrovi? 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(11):4049-926
We prove a coupled best approximations theorem in normed spaces. Also, we derive the results on coupled coincidence points and coupled fixed points, which were introduced by Lakshmikantham and ?iri? [V. Lakshmikantham, LJ. ?iri?, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. TMA, 70 (2009) 4341-4349]. 相似文献
4.
Slobodanka Jankovi? 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(7):2591-2601
Using an old M. Krein’s result and a result concerning symmetric spaces from [S. Radenovi?, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces, Banach J. Math. Anal. 5 (1) (2011), 38-50], we show in a very short way that all fixed point results in cone metric spaces obtained recently, in which the assumption that the underlying cone is normal and solid is present, can be reduced to the corresponding results in metric spaces. On the other hand, when we deal with non-normal solid cones, this is not possible. In the recent paper [M.A. Khamsi, Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl. 2010, 7 pages, Article ID 315398, doi:10.1115/2010/315398] the author claims that most of the cone fixed point results are merely copies of the classical ones and that any extension of known fixed point results to cone metric spaces is redundant; also that underlying Banach space and the associated cone subset are not necessary. In fact, Khamsi’s approach includes a small class of results and is very limited since it requires only normal cones, so that all results with non-normal cones (which are proper extensions of the corresponding results for metric spaces) cannot be dealt with by his approach. 相似文献
5.
A coupled coincidence point result in partially ordered metric spaces for compatible mappings 总被引:1,自引:0,他引:1
Binayak S. Choudhury Amaresh Kundu 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2524-5936
In this paper we introduce the notion of compatibility of mappings in a partially ordered metric space and use this notion to establish a coupled coincidence point result. Our work extends the work of Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379-1393]. An example is also given. 相似文献
6.
Let (X,d) be a complete metric space and absolute retract for metric spaces. We prove that the common fixed points set of two multivalued operators defined on X, which have the selection property and satisfy a contraction type condition, is an absolute retract for metric spaces. 相似文献
7.
The purpose of this paper is to prove the existence of a fixed point for a pointwise eventually nonexpansive mapping in a nearly uniformly convex Banach space. This provides an affirmative answer to a question given by Kirk and Xu [W.A. Kirk, Hong-Kun Xu, Asymptotic pointwise contraction, Nonlinear Anal. 69 (2008), 4706-4712]. 相似文献
8.
In this paper we present a simple and unified approach to the fixed point results on cone symmetric spaces and metric type spaces based on symmetric spaces fixed point theory. We also give a new characterization of semi-metric spaces with open balls. 相似文献
9.
H. Aydi 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6814-6825
In this paper, coincidence and common fixed point results are established in a partially ordered cone metric space. An application of our results obtained to prove the existence of a common solution to integral equations is presented. 相似文献
10.
Xing-Hua Zhu Jian-Zhong Xiao 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(16):5475-5479
In the paper “Coupled fixed point theorems for contractions in fuzzy metric spaces” by Sedghi et al. [S. Sedghi, I. Altun, N. Shobec, Coupled fixed point theorems for contractions in fuzzy metric spaces, Nonlinear Analysis 72 (2010) 1298-1304], a coupled common fixed point result was presented. However, our purpose is to show that this result and its proof are false. We give a counterexample and also explain how to correct this result. As a modification, we state and prove a coupled fixed point theorem under some hypotheses of fuzzy metric and t-norm. 相似文献
11.
In this paper a fixed point theory is established for operators defined on Cartesian product spaces. Two abstract approaches are presented in terms of closure operators and of general functionals called measures of deviations from zero resembling the measures of noncompactness. In particular, we give vectorial versions to Mönch’s fixed point theorems. An application is included to illustrate the theory. 相似文献
12.
Nadler’s contraction principle has led to fixed point theory of set-valued contraction in non-linear analysis. Inspired by the results of Nadler, the fixed point theory of set-valued contraction has been further developed in different directions by many authors, in particular, by Reich, Mizoguchi–Takahashi, Feng–Liu and many others. In the present paper, the concept of generalized contractions for set-valued maps in metric spaces is introduced and the existence of fixed point for such a contraction are guaranteed by certain conditions. Our first result extends and generalizes the Nadler, Feng–Liu and Klim–Wardowski theorems and the second result is different from the Reich and Mizoguchi–Takahashi results. As a consequence, we derive some results related to fixed point of set-valued maps satisfying certain conditions of integral type. 相似文献
13.
Nguyen Van Luong Nguyen Xuan Thuan 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(3):983-992
In this paper, we prove some coupled fixed point theorems for mappings having a mixed monotone property in partially ordered metric spaces. The main results of this paper are generalizations of the main results of Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379-1393]. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation. 相似文献
14.
Kada, Suzuki, and Takahashi introduced and studies the concept of ω- distance in fixed point theory. In this paper, we generalize and unify ?iri?’ and Fisher fixed points results for quasi-contractions on metric space to ω-distance on complete metric spaces. We also extend some results of Kada, Suzuki and Takahashi, and Suzuki. Our methods of proofs are new and even simpler than the corresponding methods in metric spaces. 相似文献
15.
We correct the proof of Theorem 1 in the paper in the title. 相似文献
16.
In this paper we give answers to questions on well-posedness in the generalized sense of the multivalued fixed point problem, which includes the well-posedness of Barnsley-Hutchinson map, raised in [7], [8] and [9]. 相似文献
17.
H.K. Pathak 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):6068-6076
In this paper, we introduce the concept of generalized quasicontraction mappings in an abstract metric space. By using this concept, we construct an iterative process which converges to a unique fixed point of these mappings. The result presented in this paper generalizes the Banach contraction principle in the setting of metric space and a recent result of Huang-Zhang for contractions. We also validate our main result by an example. 相似文献
18.
Daniela PaesanoPasquale Vetro 《Topology and its Applications》2012,159(3):911-920
Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008) 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. In this paper we prove an analogous fixed point result for a self-mapping on a partial metric space or on a partially ordered metric space. Our results on partially ordered metric spaces generalize and extend some recent results of Ran and Reurings [A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], Nieto and Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239]. We deduce, also, common fixed point results for two self-mappings. Moreover, using our results, we obtain a characterization of partial metric 0-completeness in terms of fixed point theory. This result extends Suzuki?s characterization of metric completeness. 相似文献
19.
Dragan ?ori? Stojan Radenovi? 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):1927-1932
Generalizations of the Edelstein-Suzuki theorem [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal. TMA 71 (2009), 5313-5317], including versions of the Kannan, Chatterjea and Hardy-Rogers-type fixed point results for compact metric spaces, are proved. Also, abstract metric versions of these results are obtained. Examples are presented to distinguish our results from the existing ones. 相似文献
20.
Tania A. Lazăr Adrian Petruşel Naseer Shahzad 《Nonlinear Analysis: Theory, Methods & Applications》2009
The purpose of this paper is to discuss some basic problems of the fixed point theory for non-self (single-valued and multivalued) generalized contractions. As consequences, new open operator principles and domain invariance theorems are obtained. The results complement and extend some known results in the literature. 相似文献