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Hyers–Ulam stability of integral equations with infinite delay 具有无限延迟的积分方程的 Hyers-Ulam 稳定性
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-30 DOI: 10.1007/s00010-024-01080-2
Davor Dragičević, Mihály Pituk
{"title":"Hyers–Ulam stability of integral equations with infinite delay","authors":"Davor Dragičević,&nbsp;Mihály Pituk","doi":"10.1007/s00010-024-01080-2","DOIUrl":"10.1007/s00010-024-01080-2","url":null,"abstract":"<div><p>Integral equations with infinite delay are considered as functional equations in a Banach space. Two types of Hyers–Ulam stability criteria are established. First, it is shown that a linear autonomous equation is Hyers–Ulam stable if and only if it has no characteristic value with zero real part. Second, it is proved that the Hyers–Ulam stability of a linear autonomous equation is preserved under sufficiently small nonlinear perturbations. The proofs are based on a recently developed decomposition theory of linear integral equations with infinite delay.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 5","pages":"1265 - 1280"},"PeriodicalIF":0.9,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01080-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192185","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
Smooth solutions of a class of iterative functional equations 一类迭代函数方程的平稳解
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-27 DOI: 10.1007/s00010-024-01085-x
Weiwei Shi, Xiao Tang
{"title":"Smooth solutions of a class of iterative functional equations","authors":"Weiwei Shi,&nbsp;Xiao Tang","doi":"10.1007/s00010-024-01085-x","DOIUrl":"10.1007/s00010-024-01085-x","url":null,"abstract":"<div><p>Imposing some conditions on derivatives of the known functions, using the Fiber Contraction Theorem we prove the existence of <span>(C^1)</span> solutions of a class of iterative functional equations which involves iterates of the unknown functions and a nonlinear term.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 4","pages":"941 - 951"},"PeriodicalIF":0.9,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170962","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
Another approach to K-subadditivity K 次加成的另一种方法
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-27 DOI: 10.1007/s00010-024-01083-z
Eliza Jabłońska
{"title":"Another approach to K-subadditivity","authors":"Eliza Jabłońska","doi":"10.1007/s00010-024-01083-z","DOIUrl":"10.1007/s00010-024-01083-z","url":null,"abstract":"<div><p>In the paper the notion of weakly <i>K</i>-subadditive set-valued maps is introduced in such a way that <i>F</i> is weakly <i>K</i>-superadditive if and only if <span>(-F)</span> is weakly <i>K</i>-subadditive. This new definition is a natural generalization of <i>K</i>-subadditive set-valued maps from Jabłońska and Nikodem (Aequ Math 95:1221–1231, 2021), for which opposite set-valued maps need not be <i>K</i>-subadditive. Among others, we prove that every weakly <i>K</i>-subadditive set-valued map which is <i>K</i>–upper bounded on a “large” set has to be locally weakly <i>K</i>-upper bounded and weakly <i>K</i>-lower bounded at every point of the domain. This theorem completes an analogous result for <i>K</i>-subadditive set-valued maps which are weakly <i>K</i>-upper bounded on “large” sets from Jabłońska and Nikodem (Aequ Math 95:1221–1231, 2021).</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 6","pages":"1599 - 1609"},"PeriodicalIF":0.9,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01083-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170855","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
On evolutes of curves in the isotropic plane 论各向同性平面内曲线的演变
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-25 DOI: 10.1007/s00010-024-01086-w
R. Pacheco, S. D. Santos
{"title":"On evolutes of curves in the isotropic plane","authors":"R. Pacheco, S. D. Santos","doi":"10.1007/s00010-024-01086-w","DOIUrl":"https://doi.org/10.1007/s00010-024-01086-w","url":null,"abstract":"<p>We associate to each spacelike curve in the isotropic plane a null curve in the Lorentzian 3-space. We relate the isotropic geometry of the first to the Lorentzian geometry of the second. We prove a version of the Tait–Kneser theorem for curves in the isotropic plane. Some explicit examples are given.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"41 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153218","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
Angular structure of Reuleaux cones 鲁莱欧锥的角度结构
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-25 DOI: 10.1007/s00010-024-01063-3
José Pedro Moreno, Alberto Seeger
{"title":"Angular structure of Reuleaux cones","authors":"José Pedro Moreno, Alberto Seeger","doi":"10.1007/s00010-024-01063-3","DOIUrl":"https://doi.org/10.1007/s00010-024-01063-3","url":null,"abstract":"<p>In this note we exhibit some examples of proper cones that have the property of being of constant opening angle. In particular, we analyze the class of Reuleaux cones in <span>(mathbb {R}^n)</span> with <span>(nge 3)</span>. Such cones are constructed as intersection of <i>n</i> revolutions cones <span>(textrm{Rev}(g_1,psi ),ldots , textrm{Rev}(g_n,psi ))</span> whose incenters <span>(g_1,ldots , g_n)</span> are unit vectors forming a common angle. The half-aperture angle <span>(psi )</span> of each revolution cone corresponds to the common angle between the incenters. A major result of this work is that a Reuleaux cone in <span>(mathbb {R}^n)</span> is of constant opening angle if and only if <span>(n= 3)</span>. Reuleaux cones in dimension higher than 3 are not of constant opening angle, but such mathematical objects are still of interest. In the same way that a Reuleaux triangle is a “rounded” version of an equilateral triangle, a Reuleaux cone can be viewed as a rounded version of an equiangular simplicial cone and, therefore, it has a lot of symmetry in it.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"74 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153159","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 note on homotopy extension KKM type maps 关于同调扩展 KKM 类型映射的说明
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-18 DOI: 10.1007/s00010-024-01081-1
Donal O’Regan
{"title":"A note on homotopy extension KKM type maps","authors":"Donal O’Regan","doi":"10.1007/s00010-024-01081-1","DOIUrl":"https://doi.org/10.1007/s00010-024-01081-1","url":null,"abstract":"<p>In this paper we present a variety of continuation (homotopy) theorems for general classes of maps in the literature.\u0000</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"2010 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060702","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
The Rhodes semilattice of a biased graph 偏置图的罗得半网格
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-15 DOI: 10.1007/s00010-024-01039-3
Michael J. Gottstein, Thomas Zaslavsky
{"title":"The Rhodes semilattice of a biased graph","authors":"Michael J. Gottstein,&nbsp;Thomas Zaslavsky","doi":"10.1007/s00010-024-01039-3","DOIUrl":"10.1007/s00010-024-01039-3","url":null,"abstract":"<div><p>We reinterpret the Rhodes semilattices <span>(R_n({mathfrak {G}}))</span> of a group <span>({mathfrak {G}})</span> in terms of gain graphs and generalize them to all gain graphs, both as sets of partition-potential pairs and as sets of subgraphs, and for the latter, further to biased graphs. Based on this we propose four different natural lattices in which the Rhodes semilattices and its generalizations are order ideals.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 6","pages":"1677 - 1687"},"PeriodicalIF":0.9,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060703","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
Shannon’s entropy and its bounds for some a priori known equiprobable states 香农熵及其对某些先验已知等价状态的约束
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-15 DOI: 10.1007/s00010-024-01068-y
Eleutherius Symeonidis, Flavia-Corina Mitroi-Symeonidis
{"title":"Shannon’s entropy and its bounds for some a priori known equiprobable states","authors":"Eleutherius Symeonidis,&nbsp;Flavia-Corina Mitroi-Symeonidis","doi":"10.1007/s00010-024-01068-y","DOIUrl":"10.1007/s00010-024-01068-y","url":null,"abstract":"<div><p>It is known that Shannon’s entropy is nonnegative and its maximum value is reached for equiprobable events. Adding or removing impossible events does not affect Shannon’s entropy. However, if we increase the number of events and consider not necessarily all of them equiprobable, but at least as many of them as the initial number of equiprobable events, how does Shannon’s entropy change? We study the lower bound of the interval where the probability value of the a priori assumed equiprobable states must belong when the entropy increases.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 1","pages":"237 - 242"},"PeriodicalIF":0.9,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01068-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140974128","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
On an alternative additive-quadratic functional equation 关于另一种加二次函数方程
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-13 DOI: 10.1007/s00010-024-01074-0
Gian Luigi Forti, Bettina Wilkens
{"title":"On an alternative additive-quadratic functional equation","authors":"Gian Luigi Forti, Bettina Wilkens","doi":"10.1007/s00010-024-01074-0","DOIUrl":"https://doi.org/10.1007/s00010-024-01074-0","url":null,"abstract":"<p>We consider a map <i>f</i> from one abelian group into another that satisfies either an additive or quadratic functional equation on any given pair of elements of its domain. Particular emphasis is placed on the possibility that <i>f</i> itself is neither additive nor quadratic and a complete description of all those cases is obtained.\u0000</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"12 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925574","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
Behavior of convex integrand at a d-apex of its Wulff shape and approximation of spherical bodies of constant width 凸积分在其 Wulff 形的 d-apex 处的行为和恒定宽度球体的近似值
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-11 DOI: 10.1007/s00010-024-01079-9
Huhe Han
{"title":"Behavior of convex integrand at a d-apex of its Wulff shape and approximation of spherical bodies of constant width","authors":"Huhe Han","doi":"10.1007/s00010-024-01079-9","DOIUrl":"https://doi.org/10.1007/s00010-024-01079-9","url":null,"abstract":"<p>Let <span>(gamma : S^nrightarrow mathbb {R}_+)</span> be a convex integrand and <span>(mathcal {W}_gamma )</span> be the Wulff shape of <span>(gamma )</span>. A d-apex point naturally arises in a non-smooth Wulff shape, in particular, as a vertex of a convex polytope. In this paper, we study the behavior of the convex integrand at a d-apex point of its Wulff shape. We prove that <span>(gamma (P))</span> is locally maximum, and <span>(mathbb {R}_+ Pcap partial mathcal {W}_gamma )</span> is a d-apex point of <span>(mathcal {W}_gamma )</span> if and only if the graph of <span>(gamma )</span> around the d-apex point is a piece of a sphere with center <span>(frac{1}{2}gamma (P)P)</span> and radius <span>(frac{1}{2}gamma (P))</span>. As an application of the proof of this result, we prove that for any spherical convex body <i>C</i> of constant width <span>(tau &gt;pi /2)</span>, there exists a sequence <span>({C_i}_{i=1}^infty )</span> of convex bodies of constant width <span>(tau )</span>, whose boundaries consist only of arcs of circles of radius <span>(tau -frac{pi }{2})</span> and great circle arcs such that <span>(lim _{irightarrow infty }C_i=C)</span> with respect to the Hausdorff distance.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"6 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925542","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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