Aequationes Mathematicae最新文献_第5页

On the geometry of polynomials acting on the unit circle 论作用在单位圆上的多项式的几何

IF 0.7 3区数学

Aequationes Mathematicae Pub Date : 2026-05-11 DOI: 10.1007/s00010-026-01300-x

Hristo Sendov

引用次数: 0

Perturbations of Cauchy differences 柯西差的微扰

IF 0.7 3区数学

Aequationes Mathematicae Pub Date : 2026-05-11 DOI: 10.1007/s00010-026-01294-6

Eszter Gselmann, Tomasz Małolepszy, Janusz Matkowski

{"title":"Perturbations of Cauchy differences","authors":"Eszter Gselmann, Tomasz Małolepszy, Janusz Matkowski","doi":"10.1007/s00010-026-01294-6","DOIUrl":"10.1007/s00010-026-01294-6","url":null,"abstract":"<div>This paper investigates functional equations arising from perturbations of Cauchy differences. We study equations of the form <div><div>$$ f(x+y)-f(x)-f(y)=B(x,y) quad text {or} quad f(xy)-f(x)f(y) = B(x,y) $$</div></div>where B is a biadditive mapping, and also more general cases where the inhomogeneity depends on unknown functions <div><div>$$begin{aligned} f(x+y)-f(x)-f(y)&= alpha x y f(x+y)-f(x)-f(y)&= alpha (x y) f(x+y)-f(x)-f(y)&= alpha (x)alpha (y). end{aligned}$$</div></div>Our results extend previous work on the bilinearity of the Cauchy exponential difference by Alzer and Matkowski. We characterize solutions under various structural and regularity assumptions, including additive and exponential Cauchy differences, and show that solutions often reduce to additive functions, exponential polynomials, or combinations thereof. For Levi-Civita type equations, we provide explicit representations of solutions in terms of additive and exponential components. Furthermore, we determine conditions under which real-valued solutions exist and describe their forms. The paper concludes with open problems concerning generalized equations that cannot be solved by the methods presented here, suggesting directions for future research.</div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-026-01294-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147937809","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

Kamke functions for stability of interconnected systems 互联系统稳定性的Kamke函数

IF 0.7 3区数学

Aequationes Mathematicae Pub Date : 2026-04-29 DOI: 10.1007/s00010-026-01290-w

Xiaobing Gong, Xiao Tang, Weinian Zhang

引用次数: 0

Notes on the best estimates in the Ulam stability of the Cauchy functional equation 关于柯西泛函方程Ulam稳定性的最佳估计的注释

IF 0.7 3区数学

Aequationes Mathematicae Pub Date : 2026-04-29 DOI: 10.1007/s00010-026-01292-8

Janusz Brzdęk

引用次数: 0

Independent mutual-visibility coloring and related concepts 独立可见着色及相关概念

IF 0.7 3区数学

Aequationes Mathematicae Pub Date : 2026-04-18 DOI: 10.1007/s00010-026-01280-y

Boštjan Brešar, Iztok Peterin, Babak Samadi, Ismael G. Yero

{"title":"Independent mutual-visibility coloring and related concepts","authors":"Boštjan Brešar, Iztok Peterin, Babak Samadi, Ismael G. Yero","doi":"10.1007/s00010-026-01280-y","DOIUrl":"10.1007/s00010-026-01280-y","url":null,"abstract":"<div>Given a graph G, a subset (Msubseteq V(G)) is a mutual-visibility (MV) set if for every (u,vin M), there exists a u, v-geodesic whose internal vertices are not in M. We investigate proper vertex colorings of graphs whose color classes are mutual-visibility sets. The main concepts that arise in this investigation are independent mutual-visibility (IMV) sets and vertex partitions into these sets (IMV colorings). The IMV number (mu _{i}) and the IMV chromatic number (chi _{mu _{i}}) are defined as maximum and minimum cardinality taken over all IMV sets and IMV colorings, respectively. Along the way, we also continue with the study of MV chromatic number (chi _{mu }) (as the smallest number of sets in a vertex partition into MV sets), which was initiated in an earlier paper. We establish a close connection between the (I)MV chromatic numbers of subdivisions of complete graphs and Ramsey numbers (R(4^k;2)). From the computational point of view, we prove that the problems of computing (chi _{mu _{i}}) and (mu _{i}) are NP-complete, and that it is NP-hard to decide whether a graph G satisfies (mu _i(G)=alpha (G)) where (alpha (G)) is the independence number of G. Several tight bounds on (chi _{mu _{i}}), (chi _{mu }) and (mu _{i}) are given. Exact values/formulas for these parameters in some classical families of graphs are proved. In particular, we prove that (chi _{mu _{i}}(T)=chi _{mu }(T)) holds for any tree T of order at least 3, and determine their exact formulas in the case of lexicographic product graphs. Finally, we give tight bounds on the (I)MV chromatic numbers for the Cartesian and strong product graphs, which lead to exact values in some important families of product graphs.</div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-026-01280-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738124","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

Maximal and minimal nondecreasing Lipschitzian solutions of an iterative functional equation 一类迭代泛函方程的极大极小非降Lipschitzian解

IF 0.7 3区数学

Aequationes Mathematicae Pub Date : 2026-04-15 DOI: 10.1007/s00010-026-01291-9

Shu Hua Mao, Hou Yu Zhao

引用次数: 0

Best Ulam constant of a partial differential operator 偏微分算子的最佳Ulam常数

IF 0.7 3区数学

Aequationes Mathematicae Pub Date : 2026-04-13 DOI: 10.1007/s00010-026-01287-5

Adela Novac, Diana Otrocol, Dorian Popa

引用次数: 0

Block-Toeplitz Operators On the Hardy Space Induced by a Tracial Unital Banach (*)-Probability Space 由跟踪单位Banach诱导的Hardy空间上的块- toeplitz算子(*) -概率空间

IF 0.7 3区数学

Aequationes Mathematicae Pub Date : 2026-04-13 DOI: 10.1007/s00010-026-01283-9

Ilwoo Cho, Palle E. T. Jorgensen

{"title":"Block-Toeplitz Operators On the Hardy Space Induced by a Tracial Unital Banach (*)-Probability Space","authors":"Ilwoo Cho, Palle E. T. Jorgensen","doi":"10.1007/s00010-026-01283-9","DOIUrl":"10.1007/s00010-026-01283-9","url":null,"abstract":"<div>For a fixed unital Banach (*)-probability space (left( A,tau right) ), we construct a definite, or indefinite inner product space (left( A_{0},left[ ,right] _{tau }right) ), where (A_{0}=A/kerleft( tau right) ) is the quotient Banach space and (left[ ,right] _{tau }) is a definite, or indefinite inner product on (A_{0}) determined by the trace (tau ) on the unital Banach (*)-algebra A. From this Banach space (left( A_{0},left[ ,right] _{tau }right) ), a functional vector space, called the (A_{0})-Hardy space (textbf{H}_{A_{0}:2}left( D_{1}right) ), is constructed, where (D_{1}) is the open unit ball of (A_{0}). Similar to the classical Toeplitz-operator theory, one can define Toeplitz-like adjointable Banach-space operators acting on (textbf{H}_{A_{0}:2}left( D_{1}right) ). Our main results characterizes operator-theoretic properties of those Toeplitz-like operators over (left( A,tau right) ). In particular, self-adjointness, projection-property, normality, isometry-property, and unitarity are characterized as in the usual operator theory on Hilbert spaces. As application, we study free distributions of certain types of our operator-valued Toeplitz-like operators.</div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147737749","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

Asymptotically periodic and continuous solutions of a polynomial-like iterative equation 一类多项式迭代方程的渐近周期解和连续解

IF 0.7 3区数学

Aequationes Mathematicae Pub Date : 2026-04-11 DOI: 10.1007/s00010-026-01289-3

Chao Xia, Rumeng Huo, Xi Wang, Zhinan Xia

引用次数: 0

On the Ihara expression for the generalized weighted zeta function 广义加权zeta函数的Ihara表达式

IF 0.7 3区数学

Aequationes Mathematicae Pub Date : 2026-04-09 DOI: 10.1007/s00010-026-01288-4

Ayaka Ishikawa, Hideaki Morita

引用次数: 0