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1.
In this paper, we introduce the notion of asymptotic contraction of Meir–Keeler type, and prove a fixed-point theorem for such contractions, which is a generalization of fixed-point theorems of Meir–Keeler and Kirk. In our discussion, we use the characterization of Meir–Keeler contraction proved by Lim [On characterizations of Meir–Keeler contractive maps, Nonlinear Anal. 46 (2001) 113–120]. We also give a simple proof of this characterization. 相似文献
2.
Cristina Di Bari Tomonari Suzuki Calogero Vetro 《Nonlinear Analysis: Theory, Methods & Applications》2008
We introduce a notion of cyclic Meir–Keeler contractions and prove a theorem which assures the existence and uniqueness of a best proximity point for cyclic Meir–Keeler contractions. This theorem is a generalization of a recent result due to Eldred and Veeramani. 相似文献
3.
Kazimierz Włodarczyk Robert Plebaniak Cezary Obczyński 《Nonlinear Analysis: Theory, Methods & Applications》2007
In this paper, we introduce the concepts of the set-valued dynamical systems of asymptotic contractions of Meir–Keeler type and set-valued dynamical systems of strict contractions in uniform spaces and we present a method which is useful for establishing conditions guaranteeing the existence and uniqueness of endpoints of these contractions and the convergence to these endpoints of all generalized sequences of iterations of these contractions. The result, concerning the investigations of problems of the set-valued asymptotic fixed point theory, include some well-known results of Meir and Keeler, Kirk and Suzuki concerning the asymptotic fixed point theory of single-valued maps in metric spaces. The result, concerning set-valued strict contractions (in which the contractive coefficient is not constant), is different from the result of Yuan concerning the existence of endpoints of Tarafdar–Vyborny generalized contractions (in which the contractive coefficient is constant) in bounded metric spaces and provides some examples of Tarafdar–Yuan topological contractions in compact uniform spaces. Definitions and results presented here are new for set-valued dynamical systems in uniform, locally convex and metric spaces and even for single-valued maps. Examples show a fundamental difference between our results and the well-known ones. 相似文献
4.
Each metric space is a regular cone metric space. We shall extend a result about Meir–Keeler type contraction mappings on metric spaces to regular cone metric spaces. Also, we shall give some results about fixed point of weakly uniformly strict p-contraction multifunctions on regular cone metric spaces. 相似文献
5.
Kazimierz Włodarczyk Robert Plebaniak Cezary Obczyński 《Nonlinear Analysis: Theory, Methods & Applications》2007
In this paper, the concept of the set-valued dynamical systems of contractions of Meir–Keeler type in uniform spaces is introduced and conditions guaranteeing the existence and uniqueness of endpoints of these contractions and the convergence to these endpoints of all generalized sequences of iterations of these contractions are established. The definition and the result presented here are new for set-valued dynamical systems in uniform, locally convex and metric spaces and even for single-valued maps. Examples show a fundamental difference between our result and the well-known ones. 相似文献
6.
Vasile Berinde 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7347-7355
In this paper, we extend the coupled fixed point theorems for mixed monotone operators F:X×X→X obtained in [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379–1393] by significantly weakening the contractive condition involved. Our technique of proof is essentially different and more natural. An example as well as an application to periodic BVP is also given in order to illustrate the effectiveness of our generalizations. 相似文献
7.
This article is concerned with some new best proximity point theorems for principal cyclic contractive mappings, proximal cyclic contractive mappings, and proximal contractive mappings. As a consequence, an interesting fixed point theorem, due to Edelstein, for a contractive mapping is obtained from all those best proximity point theorems. 相似文献
8.
Maher Berzig 《Journal of Fixed Point Theory and Applications》2012,12(1-2):221-238
In this paper, we establish coincidence and common fixed point theorems for contractive mappings on a metric space endowed with an amorphous binary relation. The presented theorems extend the results of Samet and Turinici in [Commun. Math. Anal. 12 (2012), 82– 97] and generalize many existing results on metric and ordered metric spaces. We apply also our main results to derive coincidence and common fixed point theorems for cyclic contractive mappings. 相似文献
9.
10.
Ding Xieping 《数学年刊B辑(英文版)》1983,4(2):153-164
In this paper the author obtains several new fixed point theorems for generalized contractive type mappings by means of Kwapisz's contractive gauge function and then proves that lots of contractive type mappings are topologically equivalent to Banach contraction with given contractive constant C∈[0, 1). 相似文献
11.
A. Aliouche 《Journal of Mathematical Analysis and Applications》2008,341(1):707-719
We prove a common fixed point theorem of Gregus type for four mappings satisfying a generalized contractive condition in metric spaces using the concept of weak compatibility which generalizes theorems of [I. Altun, D. Turkoglu, B.E. Rhoades, Fixed points of weakly compatible mappings satisfying a general contractive condition of integral type, Fixed Point Theory Appl. 2007 (2007), article ID 17301; A. Djoudi, L. Nisse, Gregus type fixed points for weakly compatible mappings, Bull. Belg. Math. Soc. 10 (2003) 369-378; A. Djoudi, A. Aliouche, Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl. 329 (1) (2007) 31-45; P. Vijayaraju, B.E. Rhoades, R. Mohanraj, A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 15 (2005) 2359-2364; X. Zhang, Common fixed point theorems for some new generalized contractive type mappings, J. Math. Anal. Appl. 333 (2) (2007) 780-786]. We prove also a common fixed point theorem which generalizes Theorem 3.5 of [H.K. Pathak, M.S. Khan, T. Rakesh, A common fixed point theorem and its application to nonlinear integral equations, Comput. Math. Appl. 53 (2007) 961-971] and common fixed point theorems of Gregus type using a strict generalized contractive condition, a property (E.A) and a common property (E.A). 相似文献
12.
13.
In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 (1962), 74–79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces. 相似文献
14.
The main purpose of this paper is to establish some common fixed point theorems under strict contractive conditions for mappings satisfying the property (E.A) in Menger probabilistic metric spaces. As applications, we obtain the corresponding common fixed point theorems under strict contractive in metric spaces. 相似文献
15.
《Optimization》2012,61(5):799-815
In this article, strong convergence theorems by the modified viscosity approximation method associated with Meir–Keeler contractions are proved for solving fixed point problems of a nonexpansive semigroup and generalized equilibrium problems in a Hilbert space. 相似文献
16.
A note on cone metric fixed point theory and its equivalence 总被引:1,自引:0,他引:1
Wei-Shih Du 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(5):2259-2261
The main aim of this paper is to investigate the equivalence of vectorial versions of fixed point theorems in generalized cone metric spaces and scalar versions of fixed point theorems in (general) metric spaces (in usual sense). We show that the Banach contraction principles in general metric spaces and in TVS-cone metric spaces are equivalent. Our theorems also extend some results in Huang and Zhang (2007) [L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468-1476], Rezapour and Hamlbarani (2008) [Sh. Rezapour, R. Hamlbarani, Some notes on the paper Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 345 (2008) 719-724] and others. 相似文献
17.
一类新的压缩条件及不动点 总被引:1,自引:0,他引:1
舒斯会 《应用泛函分析学报》2001,3(1):83-86
给出了一个一般的压缩条件,所给的压缩条件便于应用,同时还给出满足压缩条件的自映象不动点定理。 相似文献
18.
2005年,张宪在Banach空间中通过其中的锥所定义的半序引进了序压缩算子,证明了几个相应的定理.但是在一般的度量空间中,能否定义序压缩算子,能否得到类似的结论呢?本文在度量空间X中,通过X上的泛函ψ-所定义的半序,引进了ψ--序压缩算子,并且得到了相应的不动点定理. 相似文献
19.
A. Roldán J. Martínez-Moreno C. Roldán 《Journal of Mathematical Analysis and Applications》2012,396(2):536-545
In this paper we propose a notion of coincidence point between mappings in any number of variables and we prove some existence and uniqueness fixed point theorems for nonlinear mappings verifying different kinds of contractive conditions and defined on partially ordered metric spaces. These theorems extend and clarify very recent results that can be found in [T. Gnana-Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7)(2006) 1379–1393], [V. Berinde, M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 4889–4897] and [M. Berzig, B. Samet, An extension of coupled fixed point’s concept in higher dimension and applications, Comput. Math. Appl. 63 (8) (2012) 1319–1334]. 相似文献
20.
Memudu O. Olatinwo 《Central European Journal of Mathematics》2008,6(2):335-341
In this paper, we establish some common fixed point theorems for selfmappings of a uniform space by employing both the concepts
of an A—distance and an E—distance introduced by Aamri and El Moutawakil [1] and two contractive conditions of integral type.
Our results are generalizations and extensions of the classical Banach’s fixed point theorem of [2, 3, 19], some results of
Aamri and El Moutawakil [1], Theorem 2.1 of Branciari [5] as well as a result of Jungck [7].
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