抽象空间内的随机公共不动点定理

引言 随机算子的不动点理论是随机泛函分析的重要组成部分,它是研究随机算子方程解的存在唯一性的必要工具.因此有不少作者致力于将决定性不动点理论中的某些已知结果移植到随机分析中去。 最近张石生;陈绍仲;刘作述和丁协平都分别将距离空间和G-值距离空间中某些决定性不动点定理移植到随机算子的情形,推广了[1-3]和其他人的某些结果。 本文目的是首先在G-值距离空间内建立映象和映象对的某些公共不动点定理,这些定理的特例在适当附加假设下解答了Sastry:Naidv和Rhoades提出的尚待解决的问题,(见[7,p.25]和[8]的定义149,174,199),其次将所得到的某些结果随机化,建立了几个新的随机不动点定理,它们改进和推广了[1-6]中的某些重要结果。     

一类Krasnoselskii型不动点定理

本文给出两个新的不动点定理,其推广了著名的Krasnoselskii型的不动点定理及[6,7,9—11]中的某些近代的结果。     

SST—PM空间与拓扑空间之积上映射的不动点定理

本文利用作者[2]的结果给出 SST-PM 空间[1]与拓扑空间之积上映射的几个不动点定理,它们以张石生[3]中的某些主要结果为特例。     

随机积分和微分方程解的存在性准则

在[1]中我们已证明了一个一般的随机不动点定理并给出了某些应用,在本文中我们将给出该结果的进一步应用.首先证明了一随机Darbo不动点定理,然后利用此定理在紧性假设下给出了非线性随机Volterra积分方程和非线性随机微分方程Cauchy问题随机解的存在性准则.我们的定理改进和推广了Lakshmikantham[3,4],Vaugham[2],De Blasi和Myjak[5]等人的结果.     

关于一类映象的Ishikawa迭代程序的收敛性

一、引言 自1970年Dotson在[10]中引入拟非扩张映象的概念后,近几年不少人分别在引文[1—10]中讨论过某些特殊类型的拟非扩张映象的不动点的存在性及其Mann-Ishikawa迭代程序的收敛问题。 本文的目的是讨论更广泛的一类拟非扩张映射族的公共不动点的存在性,以及其Ishikawa迭代程序向该类映象象族的公共不动点的强、弱收敛性。本文的结果改进和推广了最近不少人的重要结果。     

概率内积空间中映象的不动点定理

本文的目的一是对概率度量空间引入一修正的定义;二是对这一空间中的映象建立了几个新的不动点定理.作为本文结果的应用,我们在第四节中讨论了L2(G)空间中Uryson算子方程解的存在性和唯一性问题.     

关于PM-空间中映象的不动点定理

本文在充分减弱对t-范数Δ的限制条件下,证明PM-空间中映象的几个新的不动点定理,统一和发展了[1—5]的某些主要结果。     

半可微半紧1-集压缩映象的正不动点的存在性

本文得到一些半可微半紧1-集压缩映象的不动点定理.这些结果是[1,2,4,5,7]中某些已知结果的推广.     

关于概率度量空间中压缩型映象对的不动点定理

Menger 1942 年提出概率度量空间的概念,近年来,Sehgal,Bharucha-Reid,Istratescu,林等对概率度量空间中压缩型映象不动点定理进行了研究。本文对概率度量空间压缩型映象对给出了几个新的不动点定理,这些结果统一和发展了[2,3,4]中的某些主要结果。     

随机泛函分析中可交换映象的随机不动点定理

随机不动点定理在随机泛函分析中是一重要问题.在可分完备的度量空间中的随机不动点定理Bharucha-Reid,王梓坤,?pa?ek,Han?,Itoh及作者等都曾进行过讨论(见[1-5,15-20,21]).在本文中我们对概率分析中可交换映象的随机不动点定理得出了几个新的结果,它推广了前述诸人工作中某些重要结果.在确定性情形也推广了Jungck[6,7,8],Das,Naik[9],Rhoades[10],及Ciric[11]的结果.     

Multidimensional fixed point theorems in partially ordered complete metric spaces

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].     

An Extension of Set-Valued Contraction Principle for Mappings on a Metric Space with a Graph and Application

In this paper, we obtain an existence theorem for fixed points of contractive set-valued mappings on a metric space endowed with a graph. This theorem unifies and extends several fixed point theorems for mappings on metric spaces and for mappings on metric spaces endowed with a graph. As an application, we obtain a theorem on the convergence of successive approximations for some linear operators on an arbitrary Banach space. This result yields the well-known Kelisky–Rivlin theorem on iterates of the Bernstein operators on C[0,1].     

Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces

In this paper, we introduce the concept of tripled fixed point for nonlinear mappings in partially ordered complete metric spaces and obtain existence, and existence and uniqueness theorems for contractive type mappings. Our results generalize and extend recent coupled fixed point theorems established by Gnana Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379-1393]. Examples to support our new results are given.     

Equivalent conditions for generalized contractions on (ordered) metric spaces

We establish a geometric lemma giving a list of equivalent conditions for some subsets of the plane. As its application, we get that various contractive conditions using the so-called altering distance functions coincide with classical ones. We consider several classes of mappings both on metric spaces and ordered metric spaces. In particular, we show that unexpectedly, some very recent fixed point theorems for generalized contractions on ordered metric spaces obtained by Harjani and Sadarangani [J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal. 72 (2010) 1188-1197], and Amini-Harandi and Emami [A. Amini-Harandi, H. Emami A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal. 72 (2010) 2238-2242] do follow from an earlier result of O’Regan and Petru?el [D. O’Regan and A. Petru?el, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl. 341 (2008) 1241-1252].     

Coincidence and common fixed point results on metric spaces endowed with an arbitrary binary relation and applications

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.     

Multivalued generalized nonlinear contractive maps and fixed points

We introduce some notions of generalized nonlinear contractive maps and prove some fixed point results for such maps. Consequently, several known fixed point results are either improved or generalized including the corresponding recent fixed point results of Ciric [L.B. Ciric, Multivalued nonlinear contraction mappings, Nonlinear Anal. 71 (2009) 2716-2723], Klim and Wardowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl. 334 (2007) 132-139], Feng and Liu [Y. Feng, S. Liu, Fixed point theorems for multivalued contractive mappings and multivalued Caristi type mappings, J. Math. Anal. Appl. 317 (2006) 103-112] and Mizoguchi and Takahashi [N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989) 177-188].     

A note on cone metric fixed point theory and its equivalence

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.     

KKM mappings in cone metric spaces and some fixed point theorems

In this paper, we define KKM mappings in cone metric spaces and define Nℜ-cone metric spaces to obtain some fixed point theorems and hence generalize the results obtained in [A. Amini, M. Fakhar, J. Zafarani, KKM mapping in metric spaces, Nonlinear Anal. 60 (2005) 1045-1052].     

Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces

In this paper, we establish two coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces. The theorems presented extend some results due to ?iri? (2009) [3]. An example is given to illustrate the usability of our results.     

Abstract metric spaces and Hardy–Rogers-type theorems

The purpose of the present paper is to establish coincidence point theorem for two mappings and fixed point theorem for one mapping in abstract metric space which satisfy contractive conditions of Hardy–Rogers type. Our results generalize fixed point theorems of Nemytzki [V.V. Nemytzki, Fixed point method in analysis, Uspekhi Mat. Nauk 1 (1936) 141–174], Edelstein [M. Edelstein, On fixed and periodic point under contractive mappings, J. Lond. Math. Soc. 37 (1962) 74–79] and Huang, Zhang [L.G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2) (2007) 1468–1476] from abstract metric spaces to symmetric spaces (Theorem 2.1) and to metric spaces (Theorem 2.4, Corollary 2.6, Corollary 2.7, Corollary 2.8). Two examples are given to illustrate the usability of our results.