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Topological Methods in Nonlinear Analysis最新文献

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Retracting a ball in $ell_1$ onto its simple spherical cap 将 $ell_1$ 中的球缩回到其简单的球帽上
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2024-03-19 DOI: 10.12775/tmna.2024.005
J. Intrakul, S. Iampiboonvatana
{"title":"Retracting a ball in $ell_1$ onto its simple spherical cap","authors":"J. Intrakul, S. Iampiboonvatana","doi":"10.12775/tmna.2024.005","DOIUrl":"https://doi.org/10.12775/tmna.2024.005","url":null,"abstract":"In this article, a notion and classification of spherical caps in the sequence space $ell_1$ are introduced, and the least Lipschitz constant of Lipschitz retractions from the unit ball onto a spherical cap is defined.\u0000In addition, an approximation of this value for the specific spherical cap, the simple spherical cap, is calculated. This approximation reveals a rough relation between these values, denoted by $kappa(alpha)$, and the answer of the optimal retraction problem for the space $ell_1$, denoted by $k_0(ell_1)$.\u0000To be precise, there exists $-1< mu< 0$ such that $k_0(ell_1)leqkappa(alpha)leq2+k_0(ell_1)$ whenever $-1< alpha< mu$; here $alpha$ is the level of spherical cap.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140228751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Kazimierz Goebel (1940-2022) 卡齐米日-戈贝尔（1940-2022）
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2024-03-19 DOI: 10.12775/tmna.2024.007
Stanisław Prus
{"title":"Kazimierz Goebel (1940-2022)","authors":"Stanisław Prus","doi":"10.12775/tmna.2024.007","DOIUrl":"https://doi.org/10.12775/tmna.2024.007","url":null,"abstract":"On the 21st of July, 2022, a remarkable mathematician and a former rector of the Maria Curie-Skłodowska University in Lublin (UMCS) – prof. Kazimierz Goebel left us","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140230851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A characterization of the family of iterated nonexpansive mappings under every renorming 迭代非展开映射族在每次重规范下的特征描述
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2024-03-19 DOI: 10.12775/tmna.2024.006
Víctor Pérez-García, F. E. Castillo-Santos
{"title":"A characterization of the family of iterated nonexpansive mappings under every renorming","authors":"Víctor Pérez-García, F. E. Castillo-Santos","doi":"10.12775/tmna.2024.006","DOIUrl":"https://doi.org/10.12775/tmna.2024.006","url":null,"abstract":"We characterize the family of iterated nonexpansive mappings that\u0000are stable under every renorming. The family of iterated nonexpansive\u0000mappings contains the family of nonexpansive mappings, it also contains\u0000quasi-nonexpansive and Suzuki's (C)-type mappings with fixed points,\u0000among others. We also give the corresponding characterizations for\u0000quasi-nonexpansive and some Suzuki's (C)-type mappings with fixed points.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140228784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Explicit models of ℓ_1-preduals and the weak* fixed point property in ℓ_1 ℓ_1-preduals的显式模型和ℓ_1中的弱*定点性质
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2024-03-10 DOI: 10.12775/tmna.2023.009
E. Casini, E. Miglierina, Łukasz Piasecki
{"title":"Explicit models of ℓ_1-preduals and the weak* fixed point property in ℓ_1","authors":"E. Casini, E. Miglierina, Łukasz Piasecki","doi":"10.12775/tmna.2023.009","DOIUrl":"https://doi.org/10.12775/tmna.2023.009","url":null,"abstract":"We provide a concrete isometric description of all the preduals of $ell_1$ \u0000for which the standard basis in $ell_1$ has a finite number of $w^*$-limit points.\u0000 Then, we apply this result to give an example of an $ell_1$-predual $X$ such\u0000 that its dual $X^*$ lacks the weak$^*$ fixed point property for nonexpansive\u0000 mappings (briefly, $w^*$-FPP), but $X$ does not contain an isometric copy \u0000of any hyperplane $W_{alpha}$ of the space $c$ of convergent sequences such\u0000 that $W_alpha$ is a predual of $ell_1$ and $W_alpha^*$ lacks the $w^*$-FPP.\u0000 This answers a question left open in the 2017 paper of the present authors.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140254971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Modular version of Goebel-Kirk theorem 戈贝尔-柯克定理的模块化版本
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2024-03-10 DOI: 10.12775/tmna.2023.059
Wojciech M. Kozlowski
{"title":"Modular version of Goebel-Kirk theorem","authors":"Wojciech M. Kozlowski","doi":"10.12775/tmna.2023.059","DOIUrl":"https://doi.org/10.12775/tmna.2023.059","url":null,"abstract":"In this paper we prove a fixed point theorem for asymptotically nonexpansive mappings acting in modular spaces. This result generalises the 1972 fixed point theorem by \u0000K. Goebel and W.A. Kirk. In the process, we extend several other results (including the Milman-Pettis theorem) \u0000from the class of Banach spaces to the larger class of regular modular spaces.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140255105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fixed point for mappings of asymptotically nonexpansive type in Lebesgue spaces with variable exponents 具有可变指数的勒贝格空间中渐近非展开型映射的定点
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2024-03-10 DOI: 10.12775/tmna.2023.044
Tomas Domínguez Benavides
{"title":"Fixed point for mappings of asymptotically nonexpansive type in Lebesgue spaces with variable exponents","authors":"Tomas Domínguez Benavides","doi":"10.12775/tmna.2023.044","DOIUrl":"https://doi.org/10.12775/tmna.2023.044","url":null,"abstract":"Assume that $(Omega, Sigma, mu)$ is a $sigma$-finite measure space and\u0000$pcolonOmegato [1,infty]$ a variable exponent. In the case of a purely atomic\u0000 measure, we prove that the w-FPP for mappings of asymptotically nonexpansive\u0000 type in the Nakano space $ell^{p(k)}$, where $p(k)$ is a sequence in $[1,infty]$,\u0000 is equivalent to several geometric properties of the space, as weak normal structure,\u0000 the w-FPP for nonexpansive mappings and the impossibility of containing isometrically\u0000 $L^1([0,1])$. In the case of an arbitrary $sigma$-finite measure, we prove that this\u0000 characterization also holds for pointwise eventually nonexpansive mappings.\u0000To determine if the w-FPP for nonexpansive mappings and for mappings of asymptotically nonexpansive type are equivalent is a long standing open question cite{Ki3}. \u0000According to our results, this is the case, at least, for pointwise eventually nonexpansive mappings in Lebesgue spaces with variable exponents.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140254674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fixed points of $G$-monotone mappings in metric and modular spaces 度量空间和模态空间中 G$ 单调映射的定点
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2024-03-03 DOI: 10.12775/tmna.2024.003
Dau Hong Quan, A. Wiśnicki
{"title":"Fixed points of $G$-monotone mappings in metric and modular spaces","authors":"Dau Hong Quan, A. Wiśnicki","doi":"10.12775/tmna.2024.003","DOIUrl":"https://doi.org/10.12775/tmna.2024.003","url":null,"abstract":"Let $C$ be a bounded, closed and convex subset of a reflexive metric space with a digraph $G$ such that $G$-intervals along walks are closed and convex. \u0000In the main theorem we show that if $Tcolon Crightarrow C$ is a monotone $G$-nonexpansive mapping and there exists $cin C$ such that $Tcin [c,rightarrow )_{G}$, \u0000then $T$ has a fixed point provided for each $ain C$, $[a,a]_{G}$ has the fixed point property for nonexpansive mappings. \u0000In particular, it gives an essential generalization of the Dehaish-Khamsi theorem concerning partial orders in complete uniformly convex hyperbolic metric spaces. \u0000Some counterparts of this result for modular spaces, and for commutative families of mappings are given too.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140081090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Borel linear subspace of R^omega that cannot be covered by countably many closed Haar-meager sets R^omega 的布尔线性子空间，不能被可计数的闭哈马集覆盖
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2024-03-03 DOI: 10.12775/tmna.2023.002
Taras Banakh, Eliza Jabłońska
{"title":"A Borel linear subspace of R^omega that cannot be covered by countably many closed Haar-meager sets","authors":"Taras Banakh, Eliza Jabłońska","doi":"10.12775/tmna.2023.002","DOIUrl":"https://doi.org/10.12775/tmna.2023.002","url":null,"abstract":"We prove that the countable product of lines contains a Haar-null Haar-meager \u0000Borel linear subspace $L$\u0000that cannot be covered by countably many closed Haar-meager sets.\u0000This example is applied to studying the interplay between various classes of ``large''\u0000sets and Kuczma-Ger classes in the topological vector spaces ${mathbb R}^n$ for $nle omega$.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140267203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sectional category of maps related to finite spaces 与有限空间有关的映射的部分类别
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2024-03-03 DOI: 10.12775/tmna.2023.029
Kohei Tanaka
{"title":"Sectional category of maps related to finite spaces","authors":"Kohei Tanaka","doi":"10.12775/tmna.2023.029","DOIUrl":"https://doi.org/10.12775/tmna.2023.029","url":null,"abstract":"In this study, we compute some examples of sectional category secat$(f)$\u0000and sectional number sec$(f) for continuous maps $f$ related to finite spaces.\u0000Moreover, we introduce an invariant secat$_k(f)$ for a map $f$ between finite\u0000 spaces using the $k$-th barycentric subdivision and show the equality\u0000secat$_k(f)=$ secat$(mathcal{B}(f))$ for sufficiently large $k$, where $mathcal{B}(f)$\u0000is the induced map on the associated polyhedra.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140266997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Normalized solutions to a class of Choquard-type equations with potential 一类带势能的乔夸德方程的归一化解
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2024-03-03 DOI: 10.12775/tmna.2023.028
Lei Long, Xiaojing Feng
{"title":"Normalized solutions to a class of Choquard-type equations with potential","authors":"Lei Long, Xiaojing Feng","doi":"10.12775/tmna.2023.028","DOIUrl":"https://doi.org/10.12775/tmna.2023.028","url":null,"abstract":"In this paper, we study the existence and nonexistence of solutions\u0000to the following Choquard-type equation\u0000begin{equation*}\u0000-Delta u+(V+lambda)u=(I_alpha*F(u))f(u)quadtext{in } mathbb{R}^N,\u0000end{equation*}\u0000having prescribed mass $int_{mathbb{R}^N}u^2=a$, where\u0000$lambdainmathbb{R}$ will arise as a Lagrange multiplier, $Ngeq 3$,\u0000$alphain(0,N)$, $I_alpha$ is Riesz potential. Under suitable assumptions\u0000on the potential function $V$ and the nonlinear term $f$, $a_0in[0,infty)$\u0000exists such that the above equation has a positive ground state normalized solution\u0000 if $ain(a_0,infty)$ and one has no ground state normalized solution\u0000 if $ain(0,a_0)$ when $a_0> 0$ by comparison arguments. Moreover,\u0000 we obtain sufficient conditions for $a_0=0$.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140081053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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