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A note on convex solutions to an equation on open intervals 关于开区间方程凸解的说明
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-02-24 DOI: 10.1007/s00010-024-01038-4
Chaitanya Gopalakrishna
{"title":"A note on convex solutions to an equation on open intervals","authors":"Chaitanya Gopalakrishna","doi":"10.1007/s00010-024-01038-4","DOIUrl":"10.1007/s00010-024-01038-4","url":null,"abstract":"<div><p>The note is concerned with the functional equation </p><div><div><span>$$begin{aligned} lambda _1H_1(f(x))+lambda _2H_2(f^2(x))+cdots +lambda _nH_n(f^n(x))=F(x), end{aligned}$$</span></div></div><p>which is a generalised form of the so-called polynomial-like iterative equation. We investigate the existence of nondecreasing convex (both usual and higher order) solutions to this equation on open intervals using the Schauder fixed point theorem. The results supplement those proved by Trif (Aquat Math, 79:315–327, 2010) for the polynomial-like iterative equation by generalising them to a greater extent. This assertion is supported by some examples illustrating their applicability.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 4","pages":"1151 - 1159"},"PeriodicalIF":0.9,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139953243","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
Zonal labelings and Tait colorings from a new perspective 从新的角度看带状标记和泰特着色
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-02-21 DOI: 10.1007/s00010-024-01037-5
Andrew Bowling, Weiguo Xie
{"title":"Zonal labelings and Tait colorings from a new perspective","authors":"Andrew Bowling,&nbsp;Weiguo Xie","doi":"10.1007/s00010-024-01037-5","DOIUrl":"10.1007/s00010-024-01037-5","url":null,"abstract":"<div><p>Let <span>(G=(V(G), E(G), F(G)))</span> be a plane graph with vertex, edge, and region sets <i>V</i>(<i>G</i>), <i>E</i>(<i>G</i>),  and <i>F</i>(<i>G</i>) respectively. A zonal labeling of a plane graph <i>G</i> is a labeling <span>(ell : V(G)rightarrow {1,2}subset mathbb {Z}_3)</span> such that for every region <span>(Rin F(G))</span> with boundary <span>(B_R)</span>, <span>(sum _{vin V(B_R)}ell (v)=0)</span> in <span>(mathbb {Z}_3)</span>. It has been proven by Chartrand, Egan, and Zhang that a cubic map has a zonal labeling if and only if it has a 3-edge coloring, also known as a Tait coloring. A dual notion of cozonal labelings is defined, and an alternate proof of this theorem is given. New features of cozonal labelings and their utility are highlighted along the way. Potential extensions of results to related problems are presented.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 6","pages":"1611 - 1625"},"PeriodicalIF":0.9,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139953231","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
Homi-repair under iteration (I): removable and jumping cases 迭代（I）下的同向修复：可移动和跳跃情况
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-02-20 DOI: 10.1007/s00010-024-01035-7
Xiaohua Liu, Liu Liu, Weinian Zhang
{"title":"Homi-repair under iteration (I): removable and jumping cases","authors":"Xiaohua Liu,&nbsp;Liu Liu,&nbsp;Weinian Zhang","doi":"10.1007/s00010-024-01035-7","DOIUrl":"10.1007/s00010-024-01035-7","url":null,"abstract":"<div><p>It was found that a function with exactly one discontinuity may have a continuous iterate of second order, indicating that a discontinuity may be repaired to be a continuous one by its adjacent pair of functions of second order, called second order <img> sui-repair. If a function has more than one discontinuities, examples show that some discontinuities may be repaired to be continuous ones by the other’s adjacent pair of functions of second order, called second order <span>(C^{0})</span> homi-repair. In this paper we investigate second order <span>(C^{0})</span> homi-repairs of removable and jumping discontinuities for functions having more than one but finitely many discontinuities. We give necessary and sufficient conditions for removable and jumping discontinuities to be <span>(C^0)</span> repaired by the second order iteration.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 2","pages":"351 - 379"},"PeriodicalIF":0.9,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139917539","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
Disprove of a conjecture on the double Roman domination number 推翻关于双罗马支配数的猜想
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-02-16 DOI: 10.1007/s00010-023-01029-x
Z. Shao, R. Khoeilar, H. Karami, M. Chellali, S. M. Sheikholeslami
{"title":"Disprove of a conjecture on the double Roman domination number","authors":"Z. Shao,&nbsp;R. Khoeilar,&nbsp;H. Karami,&nbsp;M. Chellali,&nbsp;S. M. Sheikholeslami","doi":"10.1007/s00010-023-01029-x","DOIUrl":"10.1007/s00010-023-01029-x","url":null,"abstract":"<div><p>A double Roman dominating function (DRDF) on a graph <span>(G=(V,E))</span> is a function <span>(f:Vrightarrow {0,1,2,3})</span> having the property that if <span>(f(v)=0)</span>, then vertex <i>v</i> must have at least two neighbors assigned 2 under <i>f</i> or one neighbor <i>w</i> with <span>(f(w)=3)</span>, and if <span>(f(v)=1)</span>, then vertex <i>v</i> must have at least one neighbor <i>w</i> with <span>(f(w)ge 2)</span>. The weight of a DRDF is the sum of its function values over all vertices, and the double Roman domination number <span>(gamma _{dR}(G))</span> is the minimum weight of a DRDF on <i>G</i>. Khoeilar et al. (Discrete Appl. Math. 270:159–167, 2019) proved that if <i>G</i> is a connected graph of order <i>n</i> with minimum degree two different from <span>(C_{5})</span> and <span>(C_{7})</span>, then <span>(gamma _{dR}(G)le frac{11}{10}n.)</span> Moreover, they presented an infinite family of graphs <span>({mathcal {G}})</span> attaining the upper bound, and conjectured that <span>({mathcal {G}})</span> is the only family of extremal graphs reaching the bound. In this paper, we disprove this conjecture by characterizing all extremal graphs for this bound.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 1","pages":"241 - 260"},"PeriodicalIF":0.9,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139903233","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
Exponential semi-polynomials and their characterization on semigroups 指数半多项式及其在半群上的表征
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-02-13 DOI: 10.1007/s00010-024-01032-w
Bruce Ebanks
{"title":"Exponential semi-polynomials and their characterization on semigroups","authors":"Bruce Ebanks","doi":"10.1007/s00010-024-01032-w","DOIUrl":"https://doi.org/10.1007/s00010-024-01032-w","url":null,"abstract":"<p>Exponential semi-polynomials on semigroups are natural generalizations of exponential polynomials on groups. We show that several of the standard properties of exponential polynomials on groups also hold for exponential semi-polynomials on semigroups. The main result is that for topological commutative monoids <i>S</i> belonging to a certain class, a function in <i>C</i>(<i>S</i>) is an exponential semi-polynomial if and only if it is contained in a finite dimensional translation invariant linear subspace. We also show that some standard results about polynomials on commutative semigroups are in fact valid on all semigroups.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"25 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139754939","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
Generalized Vincze’s functional equations on any group in connection with the maximum functional equation 与最大函数方程有关的任意群上的广义文采函数方程
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-02-03 DOI: 10.1007/s00010-023-01031-3
Muhammad Sarfraz, Zhou Jiang, Qi Liu, Yongjin Li
{"title":"Generalized Vincze’s functional equations on any group in connection with the maximum functional equation","authors":"Muhammad Sarfraz,&nbsp;Zhou Jiang,&nbsp;Qi Liu,&nbsp;Yongjin Li","doi":"10.1007/s00010-023-01031-3","DOIUrl":"10.1007/s00010-023-01031-3","url":null,"abstract":"<div><p>In this research paper, we investigate a generalization of Vincze’s type functional equations involving several (up to four) unknown functions in connection with the maximum functional equation as </p><div><div><span>$$begin{aligned} max {psi (xy), psi (xy^{-1})}&amp;= psi (x)eta (y)+psi (y), max {psi (xy), psi (xy^{-1})}&amp;= psi (x)eta (y)+chi (y), max {psi (xy), psi (xy^{-1})}&amp;= phi (x)eta (y), max {psi (xy), psi (xy^{-1})}&amp;= phi (x)eta (y)+chi (y), end{aligned}$$</span></div></div><p>where <i>G</i> is an arbitrary group, <span>(x, y in G)</span>, and <span>(psi , eta , chi , phi :G rightarrow mathbb {R})</span> are unknown functions.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 1","pages":"173 - 188"},"PeriodicalIF":0.9,"publicationDate":"2024-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139678461","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: Cosine subtraction laws 更正：余弦减法法则
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-01-29 DOI: 10.1007/s00010-023-01027-z
Bruce Ebanks
{"title":"Correction to: Cosine subtraction laws","authors":"Bruce Ebanks","doi":"10.1007/s00010-023-01027-z","DOIUrl":"10.1007/s00010-023-01027-z","url":null,"abstract":"","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 1","pages":"347 - 347"},"PeriodicalIF":0.9,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140490105","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
Vortex filament flows for curves in a 3-dimensional pseudo-Riemannian manifold 三维伪黎曼流形中曲线的涡丝流
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-01-24 DOI: 10.1007/s00010-023-01030-4
Zühal Küçükarslan Yüzbai, Nevin Ertug Gürbüz, Hyun Chul Lee, Dae Won Yoon
{"title":"Vortex filament flows for curves in a 3-dimensional pseudo-Riemannian manifold","authors":"Zühal Küçükarslan Yüzbai,&nbsp;Nevin Ertug Gürbüz,&nbsp;Hyun Chul Lee,&nbsp;Dae Won Yoon","doi":"10.1007/s00010-023-01030-4","DOIUrl":"10.1007/s00010-023-01030-4","url":null,"abstract":"<div><p>In this work, we focus on the evolution of the vortex filament flow <span>(frac{partial gamma }{partial t} = frac{partial gamma }{partial s} wedge frac{D}{ds}frac{partial gamma }{partial s})</span> for spacelike and timelike curves in a 3-dimensional pseudo-Riemannian manifold. We study the relations between a partial differential equation and the vortex filament flow for spacelike and timelike curves. As a result, we prove that the vortex filament flow of the spacelike curve in a 3-dimensional pseudo-Riemannian manifold with constant sectional curvature is equivalent to the heat equation, and the flow of the timelike curve is equivalent to the non-linear Schrödinger equation. Also, we give some examples to illustrate the vortex filament flow.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 1","pages":"261 - 274"},"PeriodicalIF":0.9,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139559943","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
(varepsilon )-isometries in (l^n_1) $$l^n_1$$ 中的 $$varepsilon $$ 等分线
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-01-17 DOI: 10.1007/s00010-023-01023-3
Igor A. Vestfrid
{"title":"(varepsilon )-isometries in (l^n_1)","authors":"Igor A. Vestfrid","doi":"10.1007/s00010-023-01023-3","DOIUrl":"10.1007/s00010-023-01023-3","url":null,"abstract":"<div><p>We show that every <span>(varepsilon )</span>-isometry of the unit ball in <span>(l^n_1)</span> can be uniformly approximated by an affine surjective isometry to within <span>(Cnvarepsilon )</span> for some absolute constant <i>C</i>.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 6","pages":"1647 - 1655"},"PeriodicalIF":0.9,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139482949","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
Notes on the arithmetic–geometric mean inequality 关于算术几何平均数不等式的说明
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-01-17 DOI: 10.1007/s00010-023-01025-1
Ahmad Al-Natoor, Omar Hirzallah, Fuad Kittaneh
{"title":"Notes on the arithmetic–geometric mean inequality","authors":"Ahmad Al-Natoor,&nbsp;Omar Hirzallah,&nbsp;Fuad Kittaneh","doi":"10.1007/s00010-023-01025-1","DOIUrl":"10.1007/s00010-023-01025-1","url":null,"abstract":"<div><p>In this paper, we give a matrix version of an equivalent form of the classical arithmetic–geometric mean inequality for two positive scalars. Applications and generalizations of our results are also given.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 6","pages":"1489 - 1502"},"PeriodicalIF":0.9,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139482887","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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