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Aequationes Mathematicae最新文献

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Uniformly-like convex solutions for the polynomial-like iterative equation in Banach spaces 巴拿赫空间多项式迭代方程的均匀类凸解
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-22 DOI: 10.1007/s00010-024-01099-5
Hou Yu Zhao, Meng Lian Xia
{"title":"Uniformly-like convex solutions for the polynomial-like iterative equation in Banach spaces","authors":"Hou Yu Zhao,&nbsp;Meng Lian Xia","doi":"10.1007/s00010-024-01099-5","DOIUrl":"10.1007/s00010-024-01099-5","url":null,"abstract":"<div><p>Using Schauder’s fixed point theorem and the Banach contraction principle, the existence, uniqueness, and stability of monotone solutions and uniformly-like convex solutions of the polynomial-like iterative functional equation are studied in Banach spaces. Furthermore, the approximate solutions of the corresponding solutions are considered. Some examples are considered for our results.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 1","pages":"199 - 221"},"PeriodicalIF":0.9,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521862","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
A Kannappan-sine subtraction law on semigroups 半群上的 Kannappan 正弦减法法则
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-22 DOI: 10.1007/s00010-024-01098-6
Ahmed Jafar, Omar Ajebbar, Elhoucien Elqorachi
{"title":"A Kannappan-sine subtraction law on semigroups","authors":"Ahmed Jafar, Omar Ajebbar, Elhoucien Elqorachi","doi":"10.1007/s00010-024-01098-6","DOIUrl":"https://doi.org/10.1007/s00010-024-01098-6","url":null,"abstract":"<p>Let <i>S</i> be a semigroup, <span>(z_0)</span> a fixed element in <i>S</i> and <span>(sigma :S longrightarrow S)</span> an involutive automorphism. We determine the complex-valued solutions of the Kannappan-sine subtraction law </p><span>$$begin{aligned} f(xsigma (y)z_0)=f(x)g(y)-f(y)g(x),; x,y in S. end{aligned}$$</span><p>As an application we solve the following variant of the Kannappan-sine subtraction law viz. </p><span>$$begin{aligned} f(xsigma (y)z_0)=f(x)g(y)-f(y)g(x)+lambda g(xsigma (y)z_0),;x,y in S, end{aligned}$$</span><p>where <span>(lambda in mathbb {C}^{*})</span>. The continuous solutions on topological semigroups are given and an example to illustrate the main results is also given.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"126 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508653","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
Elephant polynomials 大象多项式
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-22 DOI: 10.1007/s00010-024-01095-9
Hélène Guérin, Lucile Laulin, Kilian Raschel
{"title":"Elephant polynomials","authors":"Hélène Guérin, Lucile Laulin, Kilian Raschel","doi":"10.1007/s00010-024-01095-9","DOIUrl":"https://doi.org/10.1007/s00010-024-01095-9","url":null,"abstract":"<p>In this note, we study a family of polynomials that appear naturally when analysing the characteristic functions of the one-dimensional elephant random walk. These polynomials depend on a memory parameter <i>p</i> attached to the model. For certain values of <i>p</i>, these polynomials specialise to classical polynomials, such as the Chebychev polynomials in the simplest case, or generating polynomials of various combinatorial triangular arrays (e.g. Eulerian numbers). Although these polynomials are generically non-orthogonal (except for <span>(p=frac{1}{2})</span> and <span>(p=1)</span>), they have interlacing roots. Finally, we relate some algebraic properties of these polynomials to the probabilistic behaviour of the elephant random walk. Our methods are reminiscent of classical orthogonal polynomial theory and are elementary.\u0000</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"66 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532763","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
n-gon centers and central lines 核子中心和中心线
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-22 DOI: 10.1007/s00010-024-01100-1
Marta Farré Puiggalí, Luis Felipe Prieto-Martínez
{"title":"n-gon centers and central lines","authors":"Marta Farré Puiggalí,&nbsp;Luis Felipe Prieto-Martínez","doi":"10.1007/s00010-024-01100-1","DOIUrl":"10.1007/s00010-024-01100-1","url":null,"abstract":"<div><p>In this paper we provide a review of the concept of center of an <i>n</i>-gon, generalizing the original idea given by C. Kimberling for triangles. We also generalize the concept of central line for <i>n</i>-gons for <span>(nge 3)</span> and establish its basic properties.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 4","pages":"895 - 919"},"PeriodicalIF":0.9,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521863","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
Extending EP matrices by means of recent generalized inverses 通过最近的广义倒数扩展 EP 矩阵
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-21 DOI: 10.1007/s00010-024-01091-z
D. E. Ferreyra, F. E. Levis, A. N. Priori, N. Thome
{"title":"Extending EP matrices by means of recent generalized inverses","authors":"D. E. Ferreyra,&nbsp;F. E. Levis,&nbsp;A. N. Priori,&nbsp;N. Thome","doi":"10.1007/s00010-024-01091-z","DOIUrl":"10.1007/s00010-024-01091-z","url":null,"abstract":"<div><p>It is well known that a square complex matrix is called EP if it commutes with its Moore–Penrose inverse. In this paper, new classes of matrices which extend this concept are characterized. For that, we consider commutative equalities given by matrices of arbitrary index and generalized inverses recently investigated in the literature. More specifically, these classes are characterized by expressions of type <span>(A^mX=XA^m)</span>, where <i>X</i> is an outer inverse of a given complex square matrix <i>A</i> and <i>m</i> is an arbitrary positive integer. The relationships between the different classes of matrices are also analyzed. Finally, a picture presents an overview of the overall studied classes.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 4","pages":"921 - 939"},"PeriodicalIF":0.9,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01091-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Casting light on integer compositions 照亮整数组成
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-21 DOI: 10.1007/s00010-024-01094-w
Aubrey Blecher, Arnold Knopfmacher, Michael Mays
{"title":"Casting light on integer compositions","authors":"Aubrey Blecher,&nbsp;Arnold Knopfmacher,&nbsp;Michael Mays","doi":"10.1007/s00010-024-01094-w","DOIUrl":"10.1007/s00010-024-01094-w","url":null,"abstract":"<div><p>Integer compositions of <i>n</i> are viewed as bargraphs with <i>n</i> circular nodes or square cells in which the <i>i</i>th part of the composition <span>(x_i)</span> is given by the <i>i</i>th column of the bargraph with <span>(x_i)</span> nodes or cells. The sun is at infinity in the north west of our two dimensional model and each node/cell may or may not be lit depending on whether it stands in the shadow cast by another node/cell to its left. We study the number of lit nodes in an integer composition of <i>n</i> and later we modify this to yield the number of lit square cells. We then count the number of columns being lit which leads naturally to those cases where only the first column is lit. We prove the theorem that the generating function for the latter is the same as the generating function for compositions in which the first part is strictly smallest. This theorem has interesting <i>q</i>-series identities as corollaries which allow us to deduce in a simple way the asymptotics for both the number of lit nodes and columns as <span>(n rightarrow infty )</span>.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 1","pages":"155 - 173"},"PeriodicalIF":0.9,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01094-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Operators with a non-trivial closed invariant affine subspace 具有非三维封闭不变仿射子空间的算子
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-20 DOI: 10.1007/s00010-024-01090-0
Janko Bračič
{"title":"Operators with a non-trivial closed invariant affine subspace","authors":"Janko Bračič","doi":"10.1007/s00010-024-01090-0","DOIUrl":"10.1007/s00010-024-01090-0","url":null,"abstract":"<div><p>We are concerned with the question of the existence of an invariant proper affine subspace for an operator <i>A</i> on a complex Banach space. It turns out that the presence of the number 1 in the spectrum of <i>A</i> or in the spectrum of its adjoint operator <span>(A^*)</span> is crucial. For instance, an algebraic operator has an invariant proper affine subspace if and only if 1 is its eigenvalue. For an arbitrary operator <i>A</i>, we show that it has an invariant proper hyperplane if and only if 1 is an eigenvalue of <span>(A^*)</span>. If <i>A</i> is a power bounded operator, then every invariant proper affine subspace is contained in an invariant proper hyperplane, moreover, <i>A</i> has a non-trivial invariant cone.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 5","pages":"1305 - 1315"},"PeriodicalIF":0.9,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01090-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spherical and hyperbolic bicentric polygons 球面和双曲双心多边形
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-17 DOI: 10.1007/s00010-024-01088-8
Ren Guo
{"title":"Spherical and hyperbolic bicentric polygons","authors":"Ren Guo","doi":"10.1007/s00010-024-01088-8","DOIUrl":"https://doi.org/10.1007/s00010-024-01088-8","url":null,"abstract":"<p>Relations of circumradius, inradius and the distance between the circumcenter and incenter of Euclidean bicentric polygons are generalized into spherical geometry and hyperbolic geometry. The asymptotic behavior of these generalized formulas with small circumradius are studied. Relations for hyperbolic hyper-ideal bicentric polygons are derived.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"166 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508655","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
Bernoulli numbers with level 2 伯努利数第 2 级
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-13 DOI: 10.1007/s00010-024-01089-7
Takao Komatsu
{"title":"Bernoulli numbers with level 2","authors":"Takao Komatsu","doi":"10.1007/s00010-024-01089-7","DOIUrl":"10.1007/s00010-024-01089-7","url":null,"abstract":"<div><p>Stirling numbers with higher level may be considered to have been introduced by Tweedie (Proc Edinb Math Soc 37:2–25, 1918). These numbers have been recently rediscovered and studied more deeply, in particular, from combinatorial aspects. When <span>(s=2)</span>, by connecting with Stirling numbers with level 2, poly-Bernoulli numbers with level 2 may be naturally introduced as analogous to poly-Benroulli numbers. As a special case, Bernoulli numbers with level 2 are introduced and behave as an analogue of classical Bernoulli numbers. In this paper, we study Bernoulli numbers with level 2. With the help of some numbers introduced by Glaisher as well as Euler and complementary Euler numbers, we show some identities, relations and expressions for Bernoulli numbers with level 2.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 1","pages":"71 - 87"},"PeriodicalIF":0.9,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141347230","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 results on positively homogeneous subadditive functions by using Csiszár f-divergence 利用 Csiszár f-发散的正同次正函数的进一步结果
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-12 DOI: 10.1007/s00010-024-01078-w
Marek Niezgoda
{"title":"Further results on positively homogeneous subadditive functions by using Csiszár f-divergence","authors":"Marek Niezgoda","doi":"10.1007/s00010-024-01078-w","DOIUrl":"10.1007/s00010-024-01078-w","url":null,"abstract":"<div><p>In this paper, motivated by Kluza and Niezgoda (Math Inequal Appl 21(2):455–467, 2018) and Marinescu et al. (J Math Inequal 7:151–159, 2013), we prove Sherman type theorems for positively homogeneous subadditive functions of one or two variables using recent results on Csiszár’s <i>f</i>-divergence. In particular, we provide an extension of the Hardy–Littlewood–Pólya–Karamata (HLPK) theorem for such functions by replacing stochastic matrices with entrywise positive ones. As applications, we present results of HLPK type for some classical inequalities (Radon, Milne, Hölder, Minkowski, Tsallis, Hellinger), which develops the methods and theory of Marinescu et al. (2013).</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 6","pages":"1579 - 1597"},"PeriodicalIF":0.9,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141351524","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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