Tomonari Suzuki
In this short paper, we prove fixed point theorems for nonexpansive mappings whose domains are unbounded subsets of Banach spaces. These theorems are generalizations of Penot's result in [Proc. Amer. Math. Soc., 131 (2003), 2371--2377].
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Based on the technique of enriching contractive type mappings, a technique that has been used successfully in some recent papers, we introduce the concept of {\it saturated} class of contractive mappings. We show that, from this perspective, the contractive type mappings in the metric fixed point theory can be separated into two distinct classes, unsaturated and saturated, and that, for any unsaturated class of mappings, the technique of enriching contractive type mappings provides genuine new fixed point results. We illustrate the concept by surveying some significant fixed point results obta…
In this paper, we study some new common fixed point results of generalized contractive non-self multi-valued mappings on complete metric space.
We generalize the results of Sehgal and Guseman for mappings on a complete metric space with a contractive iterate condition at each point.
In this paper, we prove the existence of a common end point for a pair of multivalued mappings satisfying a new generalized weakly contractive condition in a complete metric space. Our result generalizes and extends many known results.
We established a fixed-point theorem for mapping satisfying a general contractive inequality of integral type depended an another function. This theorem substantially extend the theorem due to Branciari (2003) and Rhoades (2003)
In this paper, we study the existence of fixed points for mappings defined on complete metric space (X, d) satisfying a general contractive inequality of integral type depended on another function. This conditions is analogous of Banach conditions and Branciari Theorem.
In this paper, we establish some common fixed point results for a new class of pair of contractions mappings having functions as contractive parameters, and satisfying certain commutative properties.
A new, simple and unified approach in the theory of contractive mappings was recently given by Samet \emph{et al.} (Nonlinear Anal. 75, 2012, 2154-2165) by using the concepts of $α$-$ψ$-contractive type mappings and $α$-admissible mappings in metric spaces. The purpose of this paper is to present a new class of contractive pair of mappings called generalized $α$-$ψ$ contractive pair of mappings and study various fixed point theorems for such mappings in complete metric spaces. For this, we introduce a new notion of $α$-admissible w.r.t $g$ mapping which in turn generalizes the concept of $g$-m…
In this paper some generalized mappings due to L.B. Ciric over a generalized metric space have been studied with illustrative examples. Some theorems with necessary and sufficient conditions have been proved for such mappings on that space.
The purpose of this paper is to obtain sufficient conditions for the existence of a unique fixed point of T-Kannan type mappings on complete cone metric spaces depended on another function.
Recent developments in the fixed point theory of enriched contractive mappings. A survey
本文综述富集压缩映射技术的起源、作者团队基于该技术取得的主要成果，以及其他学者在富集映射不动点理论方面的最新进展。
Some Fixed Point Results for Interpolative Contractive Mappings in $C^{\ast}$-algebra valued metric spaces
该研究在$C^{\text{*}}$-代数值完备度量空间框架下提出插值压缩映射新概念，证明了Kannan-Riech型压缩映射的不动点及公共不动点的存在性，拓展了相关不动点理论范畴。
In this article, we introduce the notions of sequentially compactness and boundedly compactness in the framework of a newly defined $b_v(s)$-metric space which is a generalization of usual metric spaces and several other abstract spaces. We establish correlations between sequentially compactness and boundedly compactness. Moreover, we prove some fixed point results of contractive mapping in this setting, from which we can deduce several analogous fixed point results. Finally, we illustrate some non-trivial examples to validate the significances and motivations of this manuscript.
In this paper we extend the coupled fixed point theorems for mixed monotone operators $F:X \times X \rightarrow X$ obtained in [T.G. Bhaskar, V. Lakshmikantham, \textit{Fixed point theorems in partially ordered metric spaces and applications}, Nonlinear Anal. \textbf{65} (2006) 1379-1393] and [N.V. Luong and N.X. Thuan, \textit{Coupled fixed points in partially ordered metric spaces and application}, Nonlinear Anal. \textbf{74} (2011) 983-992], by weakening the involved contractive condition. An example as well an application to nonlinear Fredholm integral equations are also given in order to …
Fixed Point Theory For Singh-Chatterjea Type Contractive Mappings
本文提出结合Singh扩展与Chatterjea压缩的Singh-Chatterjea压缩条件，在完备度量空间中建立映射第p次迭代的不动点定理，推广并统一了经典结果，并通过示例与数值实现验证其适用性。
In this article, we consider Kannan type contractive self-map $T$ on a metric space $(X,d)$ such that \[d(Tx,Ty)<\frac{1}{2}\{d(x,Tx)+d(y,Ty)\} \mbox{ for all } x \neq y \in X, \] and establish some new fixed point results without taking the compactness of $X$ and also without assuming continuity of $T$. Further, we anticipate a result ensuring the completeness of the space $X$ via FPP of this map. Finally, we are able to give an affirmative answer to the open question posed by J. Górnicki [\textit{Fixed point theorems for Kannan type mappings}, J. Fixed Point Theory Appl. 2017]. Apart from th…
We study Krasnoselskii-Mann style iterative algorithms for approximating fixpoints of asymptotically weakly contractive mappings, with a focus on providing generalised convergence proofs along with explicit rates of convergence. More specifically, we define a new notion of being asymptotically $ψ$-weakly contractive with modulus, and present a series of abstract convergence theorems which both generalise and unify known results from the literature. Rates of convergence are formulated in terms of our modulus of contractivity, in conjunction with other moduli and functions which form quantitativ…
This paper is a continuation to the study of generalized quasi contractive operators, essentially due to Akhtar et al. [A multi-step implicit iterative process for common fixed points of generalized C^{q}-operators in convex metric spaces, Sci. Int., 25(4) (2013), 887-891], in spaces of nonpositive sectional curvature. We aim to establish results concerning convergence characteristics of the classical iterative algorithms such as Picard, Mann, Ishikawa and Xu-Noor iterative algorithms associated with the proposed class of generalized quasi contractive operators. Moreover, we adopt the concept …
A comparison of the weakest contractive conditions for Banach and Kannan mappings
本文比较Banach和Kannan映射的最弱收敛型条件，通过Picard序列分析，证明Kannan型映射在完备度量空间中若干最弱收敛条件等价，而Banach收缩映射则不成立，且在G-完备度量空间中差异消失。
Fixed Point Theorems for Paired Contractive Mappings in $b$-Metric Spaces
本文在b-度量空间中引入配对-Chatterjea压缩概念，建立相关不动点定理，证明其恰当扩展Chatterjea型压缩，还研究配对及配对-Kannan压缩的不动点结果，通过例子说明结果适用性，扩展推广了现有不动点定理。
The major motives of this paper are to study different types of contractive mappings and also to answer an open question of Garai et al. [The contractive principle for mappings in $b_v(s)$-metric spaces, arXiv:1802.03136]. We first set up some fixed point results associated with two types of contractive mappings in $b_v(s)$-metric spaces and then we give an answer, in positive, to the open question. Most importantly, we characterize the completeness of a $b_v(s)$-metric space via fixed point property of a certain type of contractive mappings. Our results extend and generalized several importan…
Weak and Strong Convergence of an Implicit Iteration for Hemi-Contractive Semigroups in Banach Spaces
针对Banach空间中Lipschitzian半压缩和α-半压缩半群，提出隐式迭代格式逼近公共不动点，在满足Opial条件的均匀凸Banach空间中建立弱收敛，在一般Banach空间中获得强收敛，并推广到伪压缩和半压缩映射。
We introduce multivalued Górnicki mapping and various new types of multivalued enriched contractive mappings, viz., multivalued enriched Kannan mapping, multivalued enriched Chatterjea mapping, and multivalued enriched Cirić-Reich-Rus mapping. Then we establish some existence results for the fixed points of these multivalued contractive type mappings using the fixed point property of the average operator of the mappings. Furthermore, we present some data dependence results for the fixed points of mentioned classes of mappings.
Common Fixed Points via Rational $φ$-Contractive Conditions in Orbitally Complete Metric Spaces
本文利用双变量辅助函数，在轨道完备度量空间中为两对弱相容自映射建立了无需连续性假设的公共不动点定理，推广了现有结果。
T Extended Weakly Contractive, Kannan, and Geraghty Mappings Fixed Points, Equivalences,
本文提出T扩展框架，研究弱压缩、弱Kannan和Geraghty自映射的固定点，证明T扩展弱压缩类与Geraghty类等价，T扩展弱Kannan类与Kannan-Geraghty类等价，并提供Delta型比率准则和定量Picard收敛速率。
We propose a general approach to defining a contractive-like multivalued mappings $F$ which avoids any use of the Hausdorff distance between the sets $F(x)$ and $F(y)$. Various fixed point theorems are proved under a two-parameter control of the distance function $d_{F}(x)=dist(x,F(x))$ between a point $x \in X$ and the value $F(x) ßX$. Here, both parameters are numerical functions. The first one $\a\,:[0,+ı)\rightarrow [1,+ı)$ controls the distance between $x$ and some appropriate point $y \in F(x)$ in comparison with $d_{F}(x)$, whereas the second one $\b\,:[0,+ı)\rightarrow [0,1)$ estimates…
Fixed sets and fixed points in $\Lim$--spaces]{Fixed sets and fixed points for mappings in generalized $\Lim$--spaces of Fréchet
本文在公理化定义的广义Fréchet $\Lim$--空间中，借助偏序集值类距离函数研究压缩映射，并建立了Ćirić型和Caristi型广义压缩的不动集与不动点定理。
The goal of this paper is to develop some fundamental and important nonlinear analysis for single-valued mappings under the framework of p-vector spaces, in particular, for locally p-convex spaces for p in (0, 1]. More precisely, based on the fixed point theorem of single-valued continuous condensing mapping in locally p-convex spaces as the starting point, we first establish best approximation results for (single-valued) continuous condensing mappings which are then used to develop new results for three classes of nonlinear mappings consisting of 1) condensing; 2) 1-set contractive; and 3) se…
This paper investigates the fixed points and best proximity points of multivalued cyclic self-mappings in metric spaces under a generalized contractive condition involving Hausdorff distances.
Logically Contractive Mappings: Fixed Points and Event-Indexed Rates
本文提出“逻辑压缩映射”，证明扩展 Banach 原理的不动点定理，导出事件索引及迭代计数收敛速率，并推广至变因子事件，统一多种广义压缩现象。
Using the technique of enrichment of contractive type mappings by Krasnoselskij averaging, presented here for the first time, we introduce and study the class of {\it enriched nonexpansive mappings} in Hilbert spaces. In order to approximate the fixed points of enriched nonexpansive mappings we use the Krasnoselskij iteration for which we prove strong and weak convergence theorems. Examples to illustrate the richness of the new class of contractive mappings are also given. Our results in this paper extend some classical convergence theorems established by Browder and Petryshyn in [Browder, F. …
For a bounded closed convex set $K$, in this note, we study the FPP for $α$-Hölder nonexpansive maps, i.e. mappings $T\colon K\to K$ for which $\|T x -Ty\| \leq\| x - y\|^α$ for all $x, y\in K$, $α\in (0,1)$. First, we note that only finite-dimensional spaces have the Hölder-FPP. Moreover, the unit ball $B_X$ of any infinite-dimensional space fails the FPP for Hölder maps with $\mathrm{d}(T, B_X)>0$, where $\mathrm{d}(T, K)$ denotes the minimal displacement of $T$. We further show that reflexivity and weak sequential continuity are sufficient conditions to capture fixed points of Hölder-Lipsch…
In 2007 H. Long-Guang and Z. Xian, [H. Long-Guang and Z. Xian, Cone Metric Spaces and Fixed Point Theorems of Contractive Mapping, J. Math. Anal. Appl., 322(2007), 1468-1476], generalized the concept of a metric space, by introducing cone metric spaces, and obtained some fixed point theorems for mappings satisfying certain contractive conditions. The main question was "Are cone metric spaces a real generalization of metric spaces?" Throughout this paper we answer the question in the negative, proving that every cone metric space is metrizable and the equivalent metric satisfies the same contra…
In this paper, we study some features of n-normed spaces with respect to norms of its quotient spaces. We define continuous functions with respect to the norms of its quotient spaces and show that all types of continuity are equivalent. We also study contractive mappings on n- normed spaces using the same approach. In particular, we prove a fixed point theorem for contractive mappings on a closed and bounded set in an n-normed space.
In this paper, we study the existence of fixed points for mappings defined on complete (compact) metric space (X, d) satisfying a general contractive (contraction) inequality depended on another function. These conditions are analogous to Banach conditions.
A generalization of a viscosity generalized Halpern iteration scheme is analyzed. It is proven that the solution converges asymptotically strongly to a unique fixed point of an asymptotically nonexpansive mapping which drives the iteration together with a contractive self-mapping, a viscosity term and two driving external forcing terms.
In this paper, we study the existence of fixed points for mappings defined on complete, (sequentially compact) cone metric spaces, satisfying a general contractive inequality depending of two additional mappings.
In this manuscript, we claim that the newly introduced $\mathcal{F}$-metric spaces are Hausdorff and also first countable. Moreover, we assert that every separable $\mathcal{F}$-metric space is second countable. Additionally, we acquire some interesting fixed point results concerning altering distance functions for contractive-type mappings and Kannan-type contractive mappings in this exciting context. However, most of the findings are well-furnished by several non-trivial numerical examples. Finally, we raise an open problem regarding the metrizability of such kind of spaces.
Fixed Point Theorems for Set-Valued Maps with Contractive Orbits
研究豪斯多夫空间中限制于轨道时下半连续的集值映射，引入两种收缩轨道概念并建立不动点定理，表明豪斯多夫假设重要，还推广了康托尔交定理，推导了局部凸向量空间及度量前空间中集值映射的不动点定理。
We show that the super fixed point property for nonexpansive mappings and for asymptotically nonexpansive mappings in the intermediate sense are equivalent. As a consequence, we obtain fixed point theorems for asymptotically nonexpansive mappings in uniformly nonsquare and uniformly noncreasy Banach spaces. The results are generalized for commuting families of asymptotically nonexpansive mappings.
Fixed Point Theorems for Hardy--Rogers Type Multivalued Mappings in b-Metric Spaces
本文在完备b-度量空间中，通过引入距离依赖控制函数与p阶迭代，改进推广了Chaib等人的Hardy-Rogers型不动点定理，给出p-Hardy-Rogers型多值映射的存在唯一性结论并附实例验证。
This research investigates the relations between the fixed points of asymptotically contractive operators defined on complete liner metric spaces, in general, and in separable Hilbert spaces in particular and their obtained truncations of the expansions of such operators by using Schauder bases.
In this work, a new concept of nonself total asymptotically nonexpansive mapping is introduced and an iterative process is considered for two nonself totally asymptotically nonexpansive mappings. Weak and strong convergence theorems for computing common fixed points of two nonself total asymptotically nonexpansive mappings are established in the framework of Banach spaces. Finally, we give an example which show that our theorems are applicable.
We prove the existence of a fixed point for mappings which satisfy some asymptotic nonexpansive conditions in Banach spaces which are either nearly uniformly convex or they satisfy that asymptotic centers of bounded sequences are compact. Nominally, we consider pointwise eventually nonexpansive mappings, pointwise asymptotically nonexpansive mappings and asymptotically type nonexpansive. We do not assume the existence of a continuous iterated, solving some long-standing open questions about existence of a fixed point for these mappings in absence of continuity.
We introduce a large class of contractive mappings, called Suzuki Berinde type contraction. We show that any Suzuki Berinde type contraction has a fixed point and characterizes the completeness of the underlying normed space. A fixed point theorem for multivalued mapping is also obtained. These results unify, generalize and complement various known comparable results in the literature.
In this paper we extend the coupled fixed point theorems for mixed monotone operators $F:X \times X \rightarrow X$ obtained in [T.G. Bhaskar, V. Lakshmikantham, \textit{Fixed point theorems in partially ordered metric spaces and applications}, Nonlinear Anal. TMA \textbf{65} (2006) 1379-1393] by significantly weakening the involved contractive condition. Our technique of proof is essentially different and more natural. An example as well an application to periodic BVP are also given in order to illustrate the effectiveness of our generalizations.
In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence theorem due to Matsushita and Takahashi [ Appl. Math. Comput. 196 (2008) 422-425] which was established for nonexpansive mappings.
It is our aim in this article to correct the wrong impression created in the paper of A. Rafiq titled: "Convergence theorems for uniformly L-Lipschitzian Asymptotically Nonexpansive mappings" which appeared in Acta Universitatis Apulensis no. 20/2009, 183-192.
The concept of asymptotically nonexpansive mappings is an important generalization of the class of nonexpansive mappings. Implicit midpoint procedures are extremely fundamental for solving equations involving nonlinear operators. This paper studies the convergence analysis of the class of asymptotically nonexpansive mappings by the implicit midpoint iterative procedures. The necessary conditions for the convergence of the class of asymptotically nonexpansive mappings are established, by using a well-known iterative algorithm which plays important roles in the computation of fixed points of non…
A Common Fixed Point Theorem For Weakly Compatible Mappings Satisfying Property (E. A)
本文研究弱相容自映射的公共不动点存在性问题，通过修正Beg和Abbas的相关定理，证明了满足弱压缩条件与性质(E. A)的弱相容自映射对存在公共不动点，改进了已有对应结果。
It is our aim in this note to give a counter example to an argument used in the proof of the main theorem of the paper: On iterations for families of asymptotically pseudocontractive mappings, Applied Mathematics Letters, 24 (2011), 33-38 by A. Rafiq; and give an alternative condition to correct the anomaly.
In this paper, we establish coincidence fixed point and common fixed point theorems for two mapping in complete $C^*$-algebra-valued metric spaces which satisfy new contractive conditions. Some applications of our obtained results are given.
This paper provides a fixed point theorem and iterative construction of a common fixed point for a general class of nonlinear mappings in the setup of uniformly convex hyperbolic spaces. We translate a multi-step iteration, essentially due to Chidume and Ofoedu [4] in such setting for the approximation of common fixed points of a finite family of total asymptotically nonexpansive mappings. As a consequence, we establish strong and del-convergence results which extend and generalize various corresponding results announced in the current literature.
Fixed point results for mappings of asymptotically Hölder nonexpansive type
将Goebel-Kirk不动点定理推广到渐近Hölder非扩张型映射，通过例子说明新框架严格包含经典情形，并证明若Banach空间包含c₀或ℓ₁的等距同构副本则此类映射的不动点性质失效，最后构造无限维Banach空间中存在无不动点的紧凸集K及其上的渐近Hölder非扩张型仿射自映射T。
We introduce a large class of mappings, called enriched contractions, which includes, amongst many other contractive type mappings, the Picard-Banach contractions and some nonexpansive mappings. We show that any enriched contraction has a unique fixed point and that this fixed point can be approximated by means of an appropriate Kransnoselskij iterative scheme. Several important results in fixed point theory are shown to be corollaries or consequences of the main results in this paper. We also study the fixed points of local enriched contractions, asymptotic enriched contractions and Maia type…
We establish a fixed point theorem for mappings of square matrices of all sizes which respect the matrix sizes and direct sums of matrices. The conclusions are stronger if such a mapping also respects matrix similarities, i.e., is a noncommutative function. As a special case, we prove the corresponding contractive mapping theorem which can be viewed as a new version of the Banach Fixed Point Theorem. This result is then applied to prove the existence and uniqueness of a solution of the initial value problem for ODEs in noncommutative spaces. As a by-product of the ideas developed in this paper…
Let $(A, B)$ be a nonempty bounded closed convex proximal parallel pair in a nearly uniformly convex Banach space and $T: A\cup B \rightarrow A\cup B$ be a continuous and asymptotically relatively nonexpansive map. We prove that there exists $x \in A\cup B$ such that $\|x - Tx\| = \emph{dist}(A, B)$ whenever $T(A) \subseteq B$, $T(B) \subseteq A$. Also, we establish that if $T(A) \subseteq A$ and $T(B) \subseteq B$, then there exist $x \in A$ and $y\in B$ such that $Tx = x$, $Ty = y$ and $\|x - y\| = \emph{dist}(A, B)$. We prove the aforesaid results when the pair $(A, B)$ has the rectangle pr…
We consider a relatively new hybrid generalized F-contraction involving a pair of mappings and utilize the same to prove a common fixed point theorem for a hybrid pair of occasionally coincidentally idempotent mappings satisfying generalized $(F,φ)$-contraction condition under common limit range property in complete metric spaces. A similar result involving a hybrid pair of mappings satisfying a Rational type Hardy-Rogers $(F,φ)$-contractive condition is also proved. Our results generalize and improve several results of the existing literature. As applications of our results, we prove two theo…
Using the technique of enrichment of contractive type mappings by Krasnoselskij averaging, introduced in [Berinde, V., {\it Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces}, Carpathian J. Math. {\bf 35} (2019), no. 3, 277-288.], we introduce the class of enriched Chatterjea contractions and prove general fixed point theorems for such contractions in the setting of a Banach space. Examples to illustrate the richness of the new class of contractions and the relationship between enriched Banach contractions, enriched Kannan contractions an…
Fixed points for uniformly asymptotically Hölder-Lipschitz mappings
该研究针对Banach空间中满足特定条件的一致渐近Hölder-Lipschitz映射，证明其在闭凸有界子集上存在不动点，并推广了相关经典定理。
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