Given a metric space $X$, we consider certain families of functions $f:Xtomathbb{R}$ having the hereditary oscillation property HSOP and the hereditary continuous restriction property HCRP on large sets. When $X$ is Polish, among them there are families of Baire measurable functions, $overline{mu}$-measurable functions (for a finite nonatomic Borel measure $mu$ on $X$) and Marczewski measurable functions. We obtain their characterizations using a class of equivalent point-set games. In similar aspects, we study cliquish functions, SZ-functions and countably continuous functions.
{"title":"Point-set games and functions with the hereditary small oscillation property","authors":"Marek Balcerzak, Tomasz Natkaniec, Piotr Szuca","doi":"arxiv-2405.15263","DOIUrl":"https://doi.org/arxiv-2405.15263","url":null,"abstract":"Given a metric space $X$, we consider certain families of functions\u0000$f:Xtomathbb{R}$ having the hereditary oscillation property HSOP and the\u0000hereditary continuous restriction property HCRP on large sets. When $X$ is\u0000Polish, among them there are families of Baire measurable functions,\u0000$overline{mu}$-measurable functions (for a finite nonatomic Borel measure\u0000$mu$ on $X$) and Marczewski measurable functions. We obtain their\u0000characterizations using a class of equivalent point-set games. In similar\u0000aspects, we study cliquish functions, SZ-functions and countably continuous\u0000functions.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mohamed Jleli, Cristina Maria Pacurar, Bessem Samet
We are concerned with the study of fixed points for mappings $T: Xto X$, where $(X,G)$ is a $G$-metric space in the sense of Mustafa and Sims. After the publication of the paper [Journal of Nonlinear and Convex Analysis. 7(2) (2006) 289--297] by Mustafa and Sims, a great interest was devoted to the study of fixed points in $G$-metric spaces. In 2012, the first and third authors observed that several fixed point theorems established in $G$-metric spaces are immediate consequences of known fixed point theorems in standard metric spaces. This observation demotivated the investigation of fixed points in $G$-metric spaces. In this paper, we open new directions in fixed point theory in $G$-metric spaces. Namely, we establish new versions of the Banach, Kannan and Reich fixed point theorems in $G$-metric spaces. We point out that the approach used by the first and third authors [Fixed Point Theory Appl. 2012 (2012) 1--7] is inapplicable in the present study. We also provide some interesting applications related to mappings contracting perimeters of triangles.
我们关注的是映射 $T: Xto X$ 的定点研究，其中 $(X,G)$ 是穆斯塔法和西姆斯意义上的 $G$ 度量空间。在穆斯塔法和西姆斯的论文[Journal of Nonlinear and Convex Analysis.2012 年，第一作者和第三作者注意到，在 $G$ 度量空间中建立的几个定点定理是标准度量空间中已知定点定理的直接后果。在本文中，我们开辟了$G$计量空间定点理论的新方向。也就是说，我们在$G$计量空间中建立了新版本的巴拿赫、卡南和里奇定点定理。我们指出，第一位和第三位作者[Fixed Point Theory Appl.我们还提供了一些与三角形周长收缩映射相关的有趣应用。
{"title":"New directions in fixed point theory in $G$-metric spaces and applications to mappings contracting perimeters of triangles","authors":"Mohamed Jleli, Cristina Maria Pacurar, Bessem Samet","doi":"arxiv-2405.11648","DOIUrl":"https://doi.org/arxiv-2405.11648","url":null,"abstract":"We are concerned with the study of fixed points for mappings $T: Xto X$,\u0000where $(X,G)$ is a $G$-metric space in the sense of Mustafa and Sims. After the\u0000publication of the paper [Journal of Nonlinear and Convex Analysis. 7(2) (2006)\u0000289--297] by Mustafa and Sims, a great interest was devoted to the study of\u0000fixed points in $G$-metric spaces. In 2012, the first and third authors\u0000observed that several fixed point theorems established in $G$-metric spaces are\u0000immediate consequences of known fixed point theorems in standard metric spaces.\u0000This observation demotivated the investigation of fixed points in $G$-metric\u0000spaces. In this paper, we open new directions in fixed point theory in\u0000$G$-metric spaces. Namely, we establish new versions of the Banach, Kannan and\u0000Reich fixed point theorems in $G$-metric spaces. We point out that the approach\u0000used by the first and third authors [Fixed Point Theory Appl. 2012 (2012) 1--7]\u0000is inapplicable in the present study. We also provide some interesting\u0000applications related to mappings contracting perimeters of triangles.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the existence of continuous (linear) operators from the Banach spaces $mathrm{Lip}_0(M)$ of Lipschitz functions on infinite metric spaces $M$ vanishing at a distinguished point and from their predual spaces $mathcal{F}(M)$ onto certain Banach spaces, including $C(K)$-spaces and the spaces $c_0$ and $ell_1$. For pairs of spaces $mathrm{Lip}_0(M)$ and $C(K)$ we prove that if they are endowed with topologies weaker than the norm topology, then usually no continuous (linear or not) surjection exists between those spaces. We show that, given a Banach space $E$, there exists a continuous operator from a Lipschitz-free space $mathcal{F}(M)$ onto $E$ if and only if $mathcal{F}(M)$ contains a subset homeomorphic to $E$ if and only if $d(M)ge d(E)$. We obtain a new characterization of the Schur property for spaces $mathcal{F}(M)$: a space $mathcal{F}(M)$ has the Schur property if and only if for every discrete metric space $N$ with cardinality $d(M)$ the spaces $mathcal{F}(M)$ and $mathcal{F}(N)$ are weakly sequentially homeomorphic. It is also showed that if a metric space $M$ contains a bilipschitz copy of the unit sphere $S_{c_0}$ of the space $c_0$, then $mathrm{Lip}_0(M)$ admits a continuous operator onto $ell_1$ and hence onto $c_0$. We provide several conditions for a space $M$ implying that $mathrm{Lip}_0(M)$ is not a Grothendieck space.
{"title":"Continuous operators from spaces of Lipschitz functions","authors":"Christian Bargetz, Jerzy Kąkol, Damian Sobota","doi":"arxiv-2405.09930","DOIUrl":"https://doi.org/arxiv-2405.09930","url":null,"abstract":"We study the existence of continuous (linear) operators from the Banach\u0000spaces $mathrm{Lip}_0(M)$ of Lipschitz functions on infinite metric spaces $M$\u0000vanishing at a distinguished point and from their predual spaces\u0000$mathcal{F}(M)$ onto certain Banach spaces, including $C(K)$-spaces and the\u0000spaces $c_0$ and $ell_1$. For pairs of spaces $mathrm{Lip}_0(M)$ and $C(K)$\u0000we prove that if they are endowed with topologies weaker than the norm\u0000topology, then usually no continuous (linear or not) surjection exists between\u0000those spaces. We show that, given a Banach space $E$, there exists a continuous\u0000operator from a Lipschitz-free space $mathcal{F}(M)$ onto $E$ if and only if\u0000$mathcal{F}(M)$ contains a subset homeomorphic to $E$ if and only if $d(M)ge\u0000d(E)$. We obtain a new characterization of the Schur property for spaces\u0000$mathcal{F}(M)$: a space $mathcal{F}(M)$ has the Schur property if and only\u0000if for every discrete metric space $N$ with cardinality $d(M)$ the spaces\u0000$mathcal{F}(M)$ and $mathcal{F}(N)$ are weakly sequentially homeomorphic. It\u0000is also showed that if a metric space $M$ contains a bilipschitz copy of the\u0000unit sphere $S_{c_0}$ of the space $c_0$, then $mathrm{Lip}_0(M)$ admits a\u0000continuous operator onto $ell_1$ and hence onto $c_0$. We provide several\u0000conditions for a space $M$ implying that $mathrm{Lip}_0(M)$ is not a\u0000Grothendieck space.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"131 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The main purpose of this study is to introduce and study two new classes of continuity called eR-continuous functions and weakly eR-continuous functions via e-regular sets. Both of the forms of continuous functions we have described are stronger than the weakly e-continuity. Furthermore, we obtain various characterizations of weakly eR-continuous functions. In addition, we examine not only the relations of these functions with some other forms of existing continuous functions, but also some of their fundamental properties.
本研究的主要目的是通过 e-regular 集合引入并研究两类新的连续函数，即 eR 连续函数和弱 eR 连续函数。我们所描述的这两种形式的连续函数都比弱 e-continuity 更强。此外，我们还得到了弱 eR 连续函数的各种特征。此外，我们不仅研究了这些函数与现有其他形式连续函数的关系，还研究了它们的一些基本性质。
{"title":"Strong Forms of Weakly e-continuous Functions","authors":"B. S. Ayhan","doi":"arxiv-2405.09294","DOIUrl":"https://doi.org/arxiv-2405.09294","url":null,"abstract":"The main purpose of this study is to introduce and study two new classes of\u0000continuity called eR-continuous functions and weakly eR-continuous functions\u0000via e-regular sets. Both of the forms of continuous functions we have described\u0000are stronger than the weakly e-continuity. Furthermore, we obtain various\u0000characterizations of weakly eR-continuous functions. In addition, we examine\u0000not only the relations of these functions with some other forms of existing\u0000continuous functions, but also some of their fundamental properties.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We will see how to define the metric $beta$, which turns the topological space of continuous functions whose domains are open subsets of a locally compact and second countable space $X$ to values in a polish space $Y$, called $(C_{od}(X,Y),tau_{iota,D})$ into a polish space.
{"title":"$Γ(X)$ as Polish Space","authors":"Edwar Alexis Ramírez Ardila","doi":"arxiv-2405.09437","DOIUrl":"https://doi.org/arxiv-2405.09437","url":null,"abstract":"We will see how to define the metric $beta$, which turns the topological\u0000space of continuous functions whose domains are open subsets of a locally\u0000compact and second countable space $X$ to values in a polish space $Y$, called\u0000$(C_{od}(X,Y),tau_{iota,D})$ into a polish space.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper examines the equivalence between various set convergences, as studied in [7, 13, 22], induced by an arbitrary bornology $mathcal{S}$ on a metric space $(X,d)$. Specifically, it focuses on the upper parts of the following set convergences: convergence deduced through uniform convergence of distance functionals on $mathcal{S}$ ($tau_{mathcal{S},d}$-convergence); convergence with respect to gap functionals determined by $mathcal{S}$ ($G_{mathcal{S},d}$-convergence); and bornological convergence ($mathcal{S}$-convergence). In particular, we give necessary and sufficient conditions on the structure of the bornology $mathcal{S}$ for the coincidence of $tau_{mathcal{S},d}^+$-convergence with $mathsf{G}_{mathcal{S},d}^+$-convergence, as well as $tau_{mathcal{S},d}^+$-convergence with $mathcal{S}^+$-convergence. A characterization for the equivalence of $tau_{mathcal{S},d}^+$-convergence and $mathcal{S}^+$-convergence, in terms of certain convergence of nets, has also been given earlier by Beer, Naimpally, and Rodriguez-Lopez in [13]. To facilitate our study, we first devise new characterizations for $tau_{mathcal{S},d}^+$-convergence and $mathcal{S}^+$-convergence, which we call their miss-type characterizations.
{"title":"Set Convergences via bornology","authors":"Yogesh Agarwal, Varun Jindal","doi":"arxiv-2405.07705","DOIUrl":"https://doi.org/arxiv-2405.07705","url":null,"abstract":"This paper examines the equivalence between various set convergences, as\u0000studied in [7, 13, 22], induced by an arbitrary bornology $mathcal{S}$ on a\u0000metric space $(X,d)$. Specifically, it focuses on the upper parts of the\u0000following set convergences: convergence deduced through uniform convergence of\u0000distance functionals on $mathcal{S}$ ($tau_{mathcal{S},d}$-convergence);\u0000convergence with respect to gap functionals determined by $mathcal{S}$\u0000($G_{mathcal{S},d}$-convergence); and bornological convergence\u0000($mathcal{S}$-convergence). In particular, we give necessary and sufficient\u0000conditions on the structure of the bornology $mathcal{S}$ for the coincidence\u0000of $tau_{mathcal{S},d}^+$-convergence with\u0000$mathsf{G}_{mathcal{S},d}^+$-convergence, as well as\u0000$tau_{mathcal{S},d}^+$-convergence with $mathcal{S}^+$-convergence. A\u0000characterization for the equivalence of $tau_{mathcal{S},d}^+$-convergence\u0000and $mathcal{S}^+$-convergence, in terms of certain convergence of nets, has\u0000also been given earlier by Beer, Naimpally, and Rodriguez-Lopez in [13]. To\u0000facilitate our study, we first devise new characterizations for\u0000$tau_{mathcal{S},d}^+$-convergence and $mathcal{S}^+$-convergence, which we\u0000call their miss-type characterizations.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper explores the conditions for determining fixed nodes in structured networks, specifically focusing on directed acyclic graphs (DAGs). We introduce several necessary and sufficient conditions for determining fixed nodes in $p$-layered DAGs. This is accomplished by defining the problem of maximum disjoint stems, based on the observation that all DAGs can be represented as hierarchical structures with a unique label for each layer. For structured networks, we discuss the importance of fixed nodes by considering their controllability against the variations of network parameters. Moreover, we present an efficient algorithm that simultaneously performs labeling and fixed node search for $p$-layered DAGs with an analysis of its time complexity. The results presented in this paper have implications for the analysis of controllability at the individual node level in structured networks.
本文探讨了在结构网络中确定固定节点的条件，尤其侧重于有向无环图（DAG）。我们介绍了在 p$ 层 DAG 中确定固定节点的必要条件和充分条件。根据所有 DAG 都可以表示为每层都有唯一标签的分层结构这一观点，我们定义了最大无连接干问题，从而实现了这一目标。对于结构网络，我们通过考虑固定节点对网络参数变化的可控性，讨论了固定节点的重要性。此外，我们还提出了一种高效算法，可同时对 $p$ 层 DAG 执行标记和固定节点搜索，并对其时间复杂度进行了分析。本文提出的结果对分析结构化网络中单个节点层面的可控性具有重要意义。
{"title":"Fixed Node Determination and Analysis in Directed Acyclic Graphs of Structured Networks","authors":"Nam-jin Park, Yeong-Ung Kim, Hyo-Sung Ahn","doi":"arxiv-2405.06236","DOIUrl":"https://doi.org/arxiv-2405.06236","url":null,"abstract":"This paper explores the conditions for determining fixed nodes in structured\u0000networks, specifically focusing on directed acyclic graphs (DAGs). We introduce\u0000several necessary and sufficient conditions for determining fixed nodes in\u0000$p$-layered DAGs. This is accomplished by defining the problem of maximum\u0000disjoint stems, based on the observation that all DAGs can be represented as\u0000hierarchical structures with a unique label for each layer. For structured\u0000networks, we discuss the importance of fixed nodes by considering their\u0000controllability against the variations of network parameters. Moreover, we\u0000present an efficient algorithm that simultaneously performs labeling and fixed\u0000node search for $p$-layered DAGs with an analysis of its time complexity. The\u0000results presented in this paper have implications for the analysis of\u0000controllability at the individual node level in structured networks.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"94 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nam-Jin Park, Seong-Ho Kwon, Yoo-Bin Bae, Byeong-Yeon Kim, Kevin L. Moore, Hyo-Sung Ahn
This paper presents new results and reinterpretation of existing conditions for strong structural controllability in a structured network determined by the zero/non-zero patterns of edges. For diffusively-coupled networks with self-loops, we first establish a necessary and sufficient condition for strong structural controllability, based on the concepts of dedicated and sharing nodes. Subsequently, we define several conditions for strong structural controllability across various graph types by decomposing them into disjoint path graphs. We further extend our findings by introducing a composition rule, facilitating the analysis of strong structural controllability in larger networks. This rule allows us to determine the strong structural controllability of connected graphs called pactus graphs (a generalization of the well-known cactus graph) by consideration of the strong structural controllability of its disjoint component graphs. In this process, we introduce the notion of a component input node, which is a state node that functions identically to an external input node. Based on this concept, we present an algorithm with approximate polynomial complexity to determine the minimum number of external input nodes required to maintain strong structural controllability in a diffusively-coupled network with self-loops.
{"title":"Composition Rules for Strong Structural Controllability and Minimum Input Problem in Diffusively-Coupled Networks","authors":"Nam-Jin Park, Seong-Ho Kwon, Yoo-Bin Bae, Byeong-Yeon Kim, Kevin L. Moore, Hyo-Sung Ahn","doi":"arxiv-2405.05557","DOIUrl":"https://doi.org/arxiv-2405.05557","url":null,"abstract":"This paper presents new results and reinterpretation of existing conditions\u0000for strong structural controllability in a structured network determined by the\u0000zero/non-zero patterns of edges. For diffusively-coupled networks with\u0000self-loops, we first establish a necessary and sufficient condition for strong\u0000structural controllability, based on the concepts of dedicated and sharing\u0000nodes. Subsequently, we define several conditions for strong structural\u0000controllability across various graph types by decomposing them into disjoint\u0000path graphs. We further extend our findings by introducing a composition rule,\u0000facilitating the analysis of strong structural controllability in larger\u0000networks. This rule allows us to determine the strong structural\u0000controllability of connected graphs called pactus graphs (a generalization of\u0000the well-known cactus graph) by consideration of the strong structural\u0000controllability of its disjoint component graphs. In this process, we introduce\u0000the notion of a component input node, which is a state node that functions\u0000identically to an external input node. Based on this concept, we present an\u0000algorithm with approximate polynomial complexity to determine the minimum\u0000number of external input nodes required to maintain strong structural\u0000controllability in a diffusively-coupled network with self-loops.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"130 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we compare quasi graphs and generalized $sin(1/x)$-type continua - two classes that generalize topological graphs and contain the Warsaw circle as a non-trivial element. We show that neither class is the subset of the other, provide the characterization and present illustrative examples. We unify both approaches by considering the class of tranched graphs, connect it with objects found in literature and describe how the topological structure of its elements restricts possible dynamics.
{"title":"Graphs with tranches: consequences for topology and dynamics","authors":"Michał Kowalewski, Piotr Oprocha","doi":"arxiv-2405.05407","DOIUrl":"https://doi.org/arxiv-2405.05407","url":null,"abstract":"In this paper we compare quasi graphs and generalized $sin(1/x)$-type\u0000continua - two classes that generalize topological graphs and contain the\u0000Warsaw circle as a non-trivial element. We show that neither class is the\u0000subset of the other, provide the characterization and present illustrative\u0000examples. We unify both approaches by considering the class of tranched graphs,\u0000connect it with objects found in literature and describe how the topological\u0000structure of its elements restricts possible dynamics.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove a Kannan-type fixed point theorem for multi-valued mappings on G-complete fuzzy metric spaces. The proof uses the Hausdorff fuzzy metric space which was introduced by Rodriguez-Lopez and Romaguera [19].
{"title":"A fixed point results of Kannan-type for multi-valued mapping on fuzzy metric spaces","authors":"Shunya Hashimoto, Aqib Saghir","doi":"arxiv-2405.04179","DOIUrl":"https://doi.org/arxiv-2405.04179","url":null,"abstract":"We prove a Kannan-type fixed point theorem for multi-valued mappings on\u0000G-complete fuzzy metric spaces. The proof uses the Hausdorff fuzzy metric space\u0000which was introduced by Rodriguez-Lopez and Romaguera [19].","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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