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The Bishop–Phelps–Bollobás Property for Weighted Holomorphic Mappings 加权全形映射的毕晓普-费尔普斯-波洛巴性质
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-11 DOI: 10.1007/s00025-024-02184-6
A. Jiménez-Vargas, M. I. Ramírez, Moisés Villegas-Vallecillos
{"title":"The Bishop–Phelps–Bollobás Property for Weighted Holomorphic Mappings","authors":"A. Jiménez-Vargas, M. I. Ramírez, Moisés Villegas-Vallecillos","doi":"10.1007/s00025-024-02184-6","DOIUrl":"https://doi.org/10.1007/s00025-024-02184-6","url":null,"abstract":"<p>Given an open subset <i>U</i> of a complex Banach space <i>E</i>, a weight <i>v</i> on <i>U</i> and a complex Banach space <i>F</i>, let <span>(H^infty _v(U,F))</span> denote the Banach space of all weighted holomorphic mappings from <i>U</i> into <i>F</i>, endowed with the weighted supremum norm. We introduce and study a version of the Bishop–Phelps–Bollobás property for <span>(H^infty _v(U,F))</span> (<span>(WH^infty )</span>-BPB property, for short). A result of Lindenstrauss type with sufficient conditions for <span>(H^infty _v(U,F))</span> to have the <span>(WH^infty )</span>-BPB property for every space <i>F</i> is stated. This is the case of <span>(H^infty _{v_p}(mathbb {D},F))</span> with <span>(pge 1)</span>, where <span>(v_p)</span> is the standard polynomial weight on <span>(mathbb {D})</span>. The study of the relations of the <span>(WH^infty )</span>-BPB property for the complex and vector-valued cases is also addressed as well as the extension of the cited property for mappings <span>(fin H^infty _v(U,F))</span> such that <i>vf</i> has a relatively compact range in <i>F</i>.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Sturm’s Comparison Theorem for Classical Discrete Orthogonal Polynomials 经典离散正交多项式的斯特姆比较定理
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-08 DOI: 10.1007/s00025-024-02180-w
A. Suzuki
{"title":"Sturm’s Comparison Theorem for Classical Discrete Orthogonal Polynomials","authors":"A. Suzuki","doi":"10.1007/s00025-024-02180-w","DOIUrl":"https://doi.org/10.1007/s00025-024-02180-w","url":null,"abstract":"<p>In an earlier work (Castillo et al. in J Math Phys 61:103505, 2020), it was established, from a hypergeometric-type difference equation, tractable sufficient conditions for the monotonicity with respect to a real parameter of zeros of classical discrete orthogonal polynomials on linear, quadratic, q-linear, and q-quadratic grids. In this work, we continue with the study of zeros of these polynomials by giving a comparison theorem of Sturm type. As an application, we analyze in a simple way some relations between the zeros of certain classical discrete orthogonal polynomials.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Blow-up Prevention by Logistic Damping in a Chemotaxis-May-Nowak Model for Virus Infection 在病毒感染的趋化-梅-诺瓦克模型中通过逻辑阻尼防止炸裂
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-08 DOI: 10.1007/s00025-024-02183-7
Yan Li, Qingshan Zhang
{"title":"Blow-up Prevention by Logistic Damping in a Chemotaxis-May-Nowak Model for Virus Infection","authors":"Yan Li, Qingshan Zhang","doi":"10.1007/s00025-024-02183-7","DOIUrl":"https://doi.org/10.1007/s00025-024-02183-7","url":null,"abstract":"<p>In this paper, we study the no-flux boundary initial-boundary problem for a three-component reaction-diffusion system originating from the classical May-Nowak model for viral infection </p><span>$$begin{aligned} {left{ begin{array}{ll} u_t=Delta u-chi nabla cdot (unabla v)+kappa -u-uw-mu u^{alpha }, v_t=Delta v-v+uw, w_t=Delta w-w+v end{array}right. } end{aligned}$$</span><p>in a smoothly bounded domain <span>(Omega subset {mathbb {R}}^n)</span>, <span>(nge 1)</span>. It is shown that for any <span>(kappa &gt;0)</span>, <span>(mu &gt;0)</span> and sufficiently regular nonnegative initial data <span>((u_0,v_0,w_0))</span>, the system possesses a unique nonnegative global bounded classical solution provided </p><span>$$begin{aligned} alpha &gt;frac{n+2}{2}. end{aligned}$$</span><p>Moreover, we show the large time behavior of the solution with respect to the size of <span>(kappa )</span>. More precisely, we prove that</p><ul>\u0000<li>\u0000<p>if <span>(kappa &lt;1+mu )</span>, there exists <span>(chi _1^*)</span> such that if <span>(|chi |le chi _1^*)</span>, then the solution satisfies </p><span>$$begin{aligned} u(cdot , t)rightarrow u_*, v(cdot , t)rightarrow 0 text{ and } w(cdot , t)rightarrow 0quad text{ as } trightarrow infty end{aligned}$$</span><p> in <span>(L^{infty }(Omega ))</span> exponentially, where <span>(u_*)</span> is the solution of algebraic equation </p><span>$$begin{aligned} kappa -y-mu y^{alpha }=0; end{aligned}$$</span>\u0000</li>\u0000<li>\u0000<p>if <span>(kappa &gt;1+mu )</span>, then there exists <span>(chi _2^*)</span> with the property that if <span>(|chi |le chi _2^*)</span>, then the solution fulfills that </p><span>$$begin{aligned} u(cdot , t)rightarrow 1, v(cdot , t)rightarrow kappa -1-mu text{ and } w(cdot , t)rightarrow kappa -1-mu quad text{ as } trightarrow infty end{aligned}$$</span><p> in <span>(L^{infty }(Omega ))</span>.</p>\u0000</li>\u0000</ul>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Contractive Multivariate Zipper Fractal Interpolation Functions 收缩多变量拉链分形插值函数
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-04 DOI: 10.1007/s00025-024-02177-5
Radu Miculescu, R. Pasupathi
{"title":"Contractive Multivariate Zipper Fractal Interpolation Functions","authors":"Radu Miculescu, R. Pasupathi","doi":"10.1007/s00025-024-02177-5","DOIUrl":"https://doi.org/10.1007/s00025-024-02177-5","url":null,"abstract":"<p>In this paper we introduce a new general multivariate fractal interpolation scheme using elements of the zipper methodology. Under the assumption that the corresponding Read-Bajraktarevic operator is well-defined, we enlarge the previous frameworks occurring in the literature, considering the constitutive functions of the iterated function system whose attractor is the graph of the interpolant to be just contractive in the last variable (so, in particular, they can be Banach contractions, Matkowski contractions, or Meir-Keeler contractions in the last variable). The main difficulty that should be overcome in this multivariate framework is the well definedness of the above mentioned operator. We provide three instances when it is guaranteed. We also display some examples that emphasize the generality of our scheme.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Correction to: On the Euler Function of Y-Coordinates of Pell Equations and Repdigits 更正：论佩尔方程 Y 坐标和重数的欧拉函数
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-02 DOI: 10.1007/s00025-024-02171-x
Adel Alahmadi, Florian Luca
{"title":"Correction to: On the Euler Function of Y-Coordinates of Pell Equations and Repdigits","authors":"Adel Alahmadi, Florian Luca","doi":"10.1007/s00025-024-02171-x","DOIUrl":"https://doi.org/10.1007/s00025-024-02171-x","url":null,"abstract":"","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141019128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Nonlinear Eigenvalue Problems for (p, 2)-Equations and Laplace Equations with Perturbations 有扰动的（p，2）方程和拉普拉斯方程的非线性特征值问题
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-04-30 DOI: 10.1007/s00025-024-02176-6
Krzysztof Bień
{"title":"Nonlinear Eigenvalue Problems for (p, 2)-Equations and Laplace Equations with Perturbations","authors":"Krzysztof Bień","doi":"10.1007/s00025-024-02176-6","DOIUrl":"https://doi.org/10.1007/s00025-024-02176-6","url":null,"abstract":"<p>We consider two types of nonlinear eigenvalue problems involving Laplace and <i>p</i>-Laplace operators <span>((p&gt;2))</span>. The main result establishes the existence of at least two nontrivial weak solutions in the case of the perturbed equation and the existence of a continuous spectrum in the case of the (<i>p</i>, 2)-equation. In both cases, variational methods play a central role in our arguments.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140830990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Strong Converse Inequality for Weighted Approximation of Functions by the Szász–Mirakjan–Kantorovich Operator 用 Szász-Mirakjan-Kantorovich 算子对函数进行加权逼近的强反演不等式
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-04-30 DOI: 10.1007/s00025-024-02179-3
Ivan Gadjev, Parvan E. Parvanov, Rumen Uluchev
{"title":"Strong Converse Inequality for Weighted Approximation of Functions by the Szász–Mirakjan–Kantorovich Operator","authors":"Ivan Gadjev, Parvan E. Parvanov, Rumen Uluchev","doi":"10.1007/s00025-024-02179-3","DOIUrl":"https://doi.org/10.1007/s00025-024-02179-3","url":null,"abstract":"<p>We investigate the weighted approximation of functions in <span>(L_p)</span>-norm by Kantorovich modifications of the classical Szász-Mirakjan operator, with weights of type <span>((1+x)^{alpha })</span>, <span>(alpha in {mathbb {R}})</span>. By using an appropriate <i>K</i>-functional we prove a strong converse inequality for the weighted error of approximation and characterize it exactly. We prove a Voronovskaya and Bernstein-type inequalities for the Szász-Mirakjan–Kantorovich operator.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140831061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Lyapunov Exponents for Generalized Szegő Cocycles 广义 Szegő Cocycles 的 Lyapunov 指数
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-04-29 DOI: 10.1007/s00025-024-02168-6
Licheng Fang, Fengpeng Wang
{"title":"Lyapunov Exponents for Generalized Szegő Cocycles","authors":"Licheng Fang, Fengpeng Wang","doi":"10.1007/s00025-024-02168-6","DOIUrl":"https://doi.org/10.1007/s00025-024-02168-6","url":null,"abstract":"<p>In this paper, we investigate the Lyapunov exponents of the generalized dynamically defined Szegő cocycle, corresponding to orthogonal polynomials on the circle with radius <span>(lambda )</span>. We give the upper and lower bounds of the top Lyapunov exponent in our setting by realification.\u0000</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Sombor Index and Sombor Spectrum of Cozero-Divisor Graph of $$mathbb Z_n$$ $$mathbb Z_n$$ Cozero-Divisor Graph 的松博指数和松博谱
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-04-29 DOI: 10.1007/s00025-024-02174-8
M. Anwar, M. R. Mozumder, M. Rashid, M. A. Raza
{"title":"Sombor Index and Sombor Spectrum of Cozero-Divisor Graph of $$mathbb Z_n$$","authors":"M. Anwar, M. R. Mozumder, M. Rashid, M. A. Raza","doi":"10.1007/s00025-024-02174-8","DOIUrl":"https://doi.org/10.1007/s00025-024-02174-8","url":null,"abstract":"<p>Let <span>(mathscr {Z}(mathscr {R})')</span> be the set of all non-unit and non-zero elements of ring <span>(mathscr {R})</span>, a commutative ring with identity <span>(1ne 0)</span>. The cozero-divisor graph of <span>(mathscr {R})</span>, denoted by the notation <span>({Gamma '(mathscr {R})})</span>, is an undirected graph with vertex set <span>(mathscr {Z}(mathscr {R})')</span>. Any two distinct vertices <i>w</i> and <i>z</i> are adjacent if and only if <span>(wnotin zmathscr {R})</span> and <span>(znotin wmathscr {R})</span>, where <span>(qmathscr {R})</span> is the ideal generated by the element <i>q</i> in <span>(mathscr {R})</span>. In this article, we evaluate the Sombor index of the graphs <span>({Gamma '(mathbb Z_n)})</span> for different values of <i>n</i>. Additionally, we compute <span>({Gamma '(mathbb Z_{n})})</span>, the cozero-divisor graph Sombor spectrum.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Further Generalizations of the (A.2) and (H.2) Supercongruences of Van Hamme 范哈姆（A.2）和（H.2）超共融的进一步概括
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-04-29 DOI: 10.1007/s00025-024-02175-7
Hanfei Song, Chun Wang
{"title":"Further Generalizations of the (A.2) and (H.2) Supercongruences of Van Hamme","authors":"Hanfei Song, Chun Wang","doi":"10.1007/s00025-024-02175-7","DOIUrl":"https://doi.org/10.1007/s00025-024-02175-7","url":null,"abstract":"<p>In this paper, in view of the transformation formulas for basic hypergeometric series and the creative microscoping method introduced by Guo and Zudilin, we establish new <i>q</i>-analogues of Van Hamme’s (A.2) and (H.2) supercongruences with two parameters</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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