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Aequationes Mathematicae最新文献

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On some generalization of Wright-convex functions 关于莱特凸函数的一些推广
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2026-07-31 DOI: 10.1007/s00010-026-01316-3
Andrzej Olbryś
{"title":"On some generalization of Wright-convex functions","authors":"Andrzej Olbryś","doi":"10.1007/s00010-026-01316-3","DOIUrl":"10.1007/s00010-026-01316-3","url":null,"abstract":"<div><p>In the present paper we introduce a notion of <span>(gamma )</span>-convexity which is a common generalization of the notion of convexity, Wright-convexity, strong convexity and many others. We introduce a notion of <span>(gamma )</span>-derivative which is connected to <span>(gamma )</span>-convex functions and we examine its properties. In the last section of the paper we give conditions which assure the continuity of an arbitrary <span>(gamma )</span>-convex function.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-026-01316-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628422","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
Limit cycles of continuous-discontinuous piecewise linear differential systems separated by one straight line 一条直线分隔的连续-不连续分段线性微分系统的极限环
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2026-07-31 DOI: 10.1007/s00010-026-01312-7
Fernanda Becatti, Jaume Llibre
{"title":"Limit cycles of continuous-discontinuous piecewise linear differential systems separated by one straight line","authors":"Fernanda Becatti,&nbsp;Jaume Llibre","doi":"10.1007/s00010-026-01312-7","DOIUrl":"10.1007/s00010-026-01312-7","url":null,"abstract":"<div><p>There are many papers dedicated to study the limit cycles of either continuous, or discontinuous piecewise linear differential systems separated by one straight line in the plane <span>(mathbb {R}^2)</span>. Here by first time we shall study the limit cycles of piecewise linear differential systems separated by one straight line in the plane <span>(mathbb {R}^2)</span> that are continuous in one component of differential system and discontinuous in the other.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-026-01312-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615097","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
Some Set-Valued Means and Their Schur-Concavity 若干集值均值及其schur -凹凸性
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2026-07-16 DOI: 10.1007/s00010-026-01311-8
Qian Zhang, Fen Wang, Yong-Guo Shi
{"title":"Some Set-Valued Means and Their Schur-Concavity","authors":"Qian Zhang,&nbsp;Fen Wang,&nbsp;Yong-Guo Shi","doi":"10.1007/s00010-026-01311-8","DOIUrl":"10.1007/s00010-026-01311-8","url":null,"abstract":"<div><p>Based on some classical means with a focus on Bajraktarević means and Cauchy means, we develop their set-valued extensions. By analyzing the monotonicity and convexity of derived functions, we get the sufficient conditions for the validity of these two classes of set-valued means. When the derivatives of the denominator functions are equal, by applying the equivalence conditions under which the inequalities of these two types of means hold, we derive the necessary and sufficient conditions for the set-valued mean to be valid. Some examples of set-valued means have been constructed based on Gini means and Stolarsky means. We also investigate sufficient conditions under which they satisfy the Schur-concavity property.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466081","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 about hyperrectangle functional equation 关于超矩形泛函方程的一个注意事项
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2026-07-07 DOI: 10.1007/s00010-026-01309-2
Xia Lin, Zhi Chun Yang, Hou Yu Zhao
{"title":"A note about hyperrectangle functional equation","authors":"Xia Lin,&nbsp;Zhi Chun Yang,&nbsp;Hou Yu Zhao","doi":"10.1007/s00010-026-01309-2","DOIUrl":"10.1007/s00010-026-01309-2","url":null,"abstract":"<div><p>In this paper, we extend the classical functional equations (such as the square, rectangle, and cube equations) to the hyperrectangle functional equation in the more general setting of groups. Using mathematical induction, we determine the explicit forms of the central solutions to this equation. The hyperrectangle functional equation naturally unifies and generalizes the Jensen-type and rectangle-type functional equations to functions of several variables. In particular, our results provide a unified characterization of the solutions for an arbitrary number <i>n</i> of variables.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465425","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
Alienation of additivity and (sigma )-multiplicativity on semigroups 半群上可加性和(sigma ) -可乘性的异化
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2026-06-27 DOI: 10.1007/s00010-026-01310-9
Sara Juiher, Brahim Fadli
{"title":"Alienation of additivity and (sigma )-multiplicativity on semigroups","authors":"Sara Juiher,&nbsp;Brahim Fadli","doi":"10.1007/s00010-026-01310-9","DOIUrl":"10.1007/s00010-026-01310-9","url":null,"abstract":"<div><p>Let <span>((S,+))</span> be a commutative semigroup, <span>(sigma )</span> an involution of <i>S</i>, and <span>(mathbb {F})</span> a field of characteristic different from 2. We find all solutions <span>(f,g: Srightarrow mathbb {F})</span> of the functional equation </p><div><div><span>$$ f(x+y)+g(x+sigma (y))=f(x)+f(y)+g(x)g(y), quad x,y in S, $$</span></div></div><p>which arises from summing, side by side, the additive Cauchy equation <span>(f(x+y)=f(x)+f(y))</span> and the equation <span>(g(x+sigma (y))=g(x)g(y))</span>. This enables us to investigate whether this equation is equivalent to the system </p><div><div><span>$$ left{ begin{array}{l} f(x+y)=f(x)+f(y) g(x+sigma (y))=g(x) g(y) end{array}right. $$</span></div></div><p>for all <span>(x,y in S)</span> (the alienation phenomenon). Additionally, we consider a related problem that couples d’Alembert’s functional equation with the additive Cauchy equation.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323723","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
Existence of solutions and stability results for a viscoelastic petrovsky equation with logarithmic variable-exponent nonlinearity 具有对数变指数非线性的粘弹性petrovsky方程解的存在性和稳定性结果
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2026-06-17 DOI: 10.1007/s00010-026-01308-3
Aissa Guesmia, Taklit HAMADOUCHE
{"title":"Existence of solutions and stability results for a viscoelastic petrovsky equation with logarithmic variable-exponent nonlinearity","authors":"Aissa Guesmia,&nbsp;Taklit HAMADOUCHE","doi":"10.1007/s00010-026-01308-3","DOIUrl":"10.1007/s00010-026-01308-3","url":null,"abstract":"<div><p>In this paper, we consider a Petrovsky equation in the presence of a logarithmic nonlinearity with a variable exponent and subject to the effect of a distributed infinite memory term. In order to deal with the presence of the memory term, we adopt the history approach. First, we show that our problem is well-posed in appropriate functional spaces by means of the semigroup theory provided that the initial data are sufficiently small and the variable exponent satisfies some specific smoothness and boundedness conditions. Then, we establish explicit and general decay results for a wide class of relaxation functions having an arbitrary growth at infinity by using the multiplier method.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281119","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
Extremal Results on Bond Incident Degree Indices of Graphs: A Survey 图的键关联度指数的极值结果：综述
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2026-06-11 DOI: 10.1007/s00010-026-01306-5
Akbar Ali, Ivan Gutman, Boris Furtula
{"title":"Extremal Results on Bond Incident Degree Indices of Graphs: A Survey","authors":"Akbar Ali,&nbsp;Ivan Gutman,&nbsp;Boris Furtula","doi":"10.1007/s00010-026-01306-5","DOIUrl":"10.1007/s00010-026-01306-5","url":null,"abstract":"<div><p>Let <i>G</i> be a graph with edge set <i>E</i>(<i>G</i>). Denote by <span>(d_v)</span> the degree of the vertex <i>v</i> of <i>G</i>. Let <i>f</i> be a symmetric real-valued function defined on the Cartesian square of the degree set of <i>G</i>, which is the set of distinct elements of the degree sequence of <i>G</i>. The graph invariants of the form <span>(sum _{uvin E(G)}f(d_u,d_v))</span> are known as bond incident degree (BID) indices, or more generally, (vertex-)degree-based topological indices. Many existing much-studied graph invariants (in mathematical chemistry) have the aforementioned form. In a considerable number of cases, the extremal results with respect to particular BID indices, including their proofs, are quite similar. Therefore, around a decade ago, researchers started to study BID indices in a unified way, generalizing the existing results and obtaining new findings by imposing certain constraints on the function <i>f</i>. In the present survey, we summarize the current research on BID indices, particularly extremal results. Various open problems related to such indices are also provided.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148236783","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
An elementary derivation of 3-cycles for a quadratic map 二次映射的3环的初等推导
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2026-06-06 DOI: 10.1007/s00010-026-01296-4
Árpád Bényi, Ioan Caşu
{"title":"An elementary derivation of 3-cycles for a quadratic map","authors":"Árpád Bényi,&nbsp;Ioan Caşu","doi":"10.1007/s00010-026-01296-4","DOIUrl":"10.1007/s00010-026-01296-4","url":null,"abstract":"<div><p>We present an elementary derivation of the period-three cycles for the real quadratic map <span>(xmapsto x^2+c)</span>, a fundamental model in one-dimensional discrete dynamics. Using symmetric polynomials, we obtain a complete algebraic characterization of 3-cycles and determine explicit conditions for their existence and stability, without reliance on computer algebra. Through conjugacy with the logistic map, we recover the classical threshold values of the logistic parameter corresponding to the emergence and loss of stability of the 3-cycle. Our methodology outlines a transparent and algebraically grounded route to understanding the onset of chaos in quadratic and logistic dynamics.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172902","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
Zero distribution of polynomials in a quaternionic variable 四元数变量中多项式的零分布
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2026-06-06 DOI: 10.1007/s00010-026-01297-3
Gradimir V. Milovanović, Abdullah Mir
{"title":"Zero distribution of polynomials in a quaternionic variable","authors":"Gradimir V. Milovanović,&nbsp;Abdullah Mir","doi":"10.1007/s00010-026-01297-3","DOIUrl":"10.1007/s00010-026-01297-3","url":null,"abstract":"<div><p>This paper aims to construct a framework for finding the zero inclusion regions of polynomials and regular functions with quaternionic coefficients located on one side of the powers of the quaternionic variable. We will employ the extended Schwarz’s lemma, the zero sets of a regular product, and a Grešgorin-type result for the eigenvalue distribution of a quaternionic matrix. The outcomes acquired for this specific subclass of regular functions result in the generalization of further outcomes that are recognized in the relevant literature.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172899","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
On differences of square pyramidal numbers II 关于方锥体数的差异2
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2026-06-06 DOI: 10.1007/s00010-026-01305-6
Anji Dong, Katerina Saettone, Kendra Song, Alexandru Zaharescu
{"title":"On differences of square pyramidal numbers II","authors":"Anji Dong,&nbsp;Katerina Saettone,&nbsp;Kendra Song,&nbsp;Alexandru Zaharescu","doi":"10.1007/s00010-026-01305-6","DOIUrl":"10.1007/s00010-026-01305-6","url":null,"abstract":"<div><p>This paper presents some new results concerned with uniform distribution properties associated with the sequence <span>((a_n)_{nin mathbb {N}})</span>, which is defined as the distance from the <i>n</i>-th square pyramidal number to the closest square. We also extend the results to arithmetic progressions.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172984","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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