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Weakly associative functions 弱结合函数
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-07-24 DOI: 10.1007/s00010-025-01173-6
Dorota Głazowska, Janusz Matkowski
{"title":"Weakly associative functions","authors":"Dorota Głazowska,&nbsp;Janusz Matkowski","doi":"10.1007/s00010-025-01173-6","DOIUrl":"10.1007/s00010-025-01173-6","url":null,"abstract":"<div><p>Let <span>(Isubset mathbb {R})</span> be an interval. A function <span>(M:I^{2}rightarrow I)</span> is said to be <i>weakly associative</i>, if </p><div><div><span>$$begin{aligned} Mleft( Mleft( x,yright) ,xright) =Mleft( x,Mleft( y,xright) right) , qquad x,yin I. end{aligned}$$</span></div></div><p>One can easily check that every weighted quasi-arithmetic mean, i.e. a function <span>(M:I^{2}rightarrow I)</span> given by </p><div><div><span>$$ Mleft( x,yright) =f^{-1}left( pfleft( xright) +left( 1-pright) fleft( yright) right) , $$</span></div></div><p>where <span>(f:Irightarrow mathbb {R})</span> is a continuous and strictly monotonic function and <span>(pin left[ 0,1right] )</span>, satisfies the above condition, so it is weakly associative. We give the characterization of weakly associative functions in the class of some generalized weighted quasi-arithmetic means. Moreover, we characterize premeans which are rational functions of degree at most 2 and weakly associative.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"1827 - 1841"},"PeriodicalIF":0.7,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-025-01173-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110547","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
Domination parameters and added matchings 控制参数和添加的匹配
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-07-23 DOI: 10.1007/s00010-025-01196-z
Wayne Goddard, Michael A. Henning
{"title":"Domination parameters and added matchings","authors":"Wayne Goddard,&nbsp;Michael A. Henning","doi":"10.1007/s00010-025-01196-z","DOIUrl":"10.1007/s00010-025-01196-z","url":null,"abstract":"<div><p>We consider the augmentation problem of how domination parameters behave when a perfect matching <i>P</i> of the complement is added to the graph. We focus on the case that the graph is a tree, and inter alia show that if <i>T</i> is a tree of even order <i>n</i> that is not a star, then <span>(T+P)</span> has domination number at most 2<i>n</i>/5, independent domination number at most <span>(n/2-1)</span>, and total domination and upper domination number at most <i>n</i>/2. Further, there exists a choice of <i>P</i> such that <span>(T+P)</span> has total domination number at most <i>n</i>/3. All these bounds are sharp.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"2009 - 2024"},"PeriodicalIF":0.7,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110482","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 Zero–Hopf bifurcations of the quadratic polynomial differential jerk systems in ({mathbb {R}^3}) 二阶多项式微分抽动系统的零霍普夫分岔 ({mathbb {R}^3})
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-07-22 DOI: 10.1007/s00010-025-01182-5
Jaume Llibre, Ammar Makhlouf
{"title":"The Zero–Hopf bifurcations of the quadratic polynomial differential jerk systems in ({mathbb {R}^3})","authors":"Jaume Llibre,&nbsp;Ammar Makhlouf","doi":"10.1007/s00010-025-01182-5","DOIUrl":"10.1007/s00010-025-01182-5","url":null,"abstract":"<div><p>We study the zero–Hopf bifurcations of all quadratic polynomial differential jerk systems in <span>({mathbb {R}^3})</span></p><div><div><span>$$begin{aligned} begin{array}{l} dot{x}=y, dot{y}=z, dot{z}=a_{0}+a_{1}x+a_{2}y+a_{3}z+a_{4}x^{2}+a_{5}xy+a_{6}xz+a_{7}y^{2}+a_{8}yz+a_{9}z^{2}, end{array} end{aligned}$$</span></div></div><p>where the dot denotes derivative with respect to the independent variable <i>t</i> and the coefficients <span>(a_{k})</span>, for <span>(k=0,1,...,9)</span>, are real.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"1995 - 2007"},"PeriodicalIF":0.7,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-025-01182-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110514","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
Visibility polynomials, dual visibility spectrum, and characterization of total mutual-visibility sets 可见多项式、对偶可见谱和总互可见集的表征
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-07-22 DOI: 10.1007/s00010-025-01197-y
Csilla Bujtás, Sandi Klavžar, Jing Tian
{"title":"Visibility polynomials, dual visibility spectrum, and characterization of total mutual-visibility sets","authors":"Csilla Bujtás,&nbsp;Sandi Klavžar,&nbsp;Jing Tian","doi":"10.1007/s00010-025-01197-y","DOIUrl":"10.1007/s00010-025-01197-y","url":null,"abstract":"<div><p>Mutual-visibility sets were motivated by visibility in distributed systems and social networks, and intertwine with several classical mathematical areas. Monotone properties of the variety of mutual-visibility sets, and restrictions of such sets to convex and isometric subgraphs are studied. Dual mutual-visibility sets are shown to be intrinsically different from other types of mutual-visibility sets. It is proved that for every finite subset <i>Z</i> of positive integers there exists a graph <i>G</i> that has a dual mutual-visibility set of size <i>i</i> if and only if <span>(iin Zcup {0})</span>, while for the other types of mutual-visibility such a set consists of consecutive integers. Visibility polynomials are introduced and their properties derived. As a surprise, every polynomial with nonnegative integer coefficients and with a constant term 1 is a dual visibility polynomial of some graph. Characterizations are given for total mutual-visibility sets, for graphs with total mutual-visibility number 1, and for sets which are not total mutual-visibility sets, yet every proper subset is such. Along the way an earlier result from the literature is corrected.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"1883 - 1901"},"PeriodicalIF":0.7,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-025-01197-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110513","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
Convex Meir-Keeler-Ćirić-Matkowski contractive mappings and their application to functional equation arising in the behavioral study of paradise fish and predator-prey models on the Lipschitz spaces 凸Meir-Keeler-Ćirić-Matkowski收缩映射及其在天堂鱼行为研究中的函数方程和Lipschitz空间上的捕食-食饵模型中的应用
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-07-22 DOI: 10.1007/s00010-025-01199-w
Kushal Roy, Ravindra K. Bisht
{"title":"Convex Meir-Keeler-Ćirić-Matkowski contractive mappings and their application to functional equation arising in the behavioral study of paradise fish and predator-prey models on the Lipschitz spaces","authors":"Kushal Roy,&nbsp;Ravindra K. Bisht","doi":"10.1007/s00010-025-01199-w","DOIUrl":"10.1007/s00010-025-01199-w","url":null,"abstract":"<div><p>In this paper, we introduce a new class of contractive definitions known as convex Meir-Keeler-Ćirić-Matkowski contractive mappings. We establish several fixed point theorems under this new condition, allowing for both continuity and discontinuity at the fixed points. Our results not only encompass all previously known findings in this domain but also offer new insights into the continuity of contractive mappings at their fixed points. As an application of our theorem, we demonstrate the existence and uniqueness of solutions to a functional equation in the Lipschitz space. The functional equation we consider broadly encompasses various functional equations, including those recently studied for analyzing the two-choice behavior of the paradise fish and for solving models involving two prey species and one predator.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"1565 - 1584"},"PeriodicalIF":0.7,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110515","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
More results on the signed double Roman k-domination in graphs 图中符号双罗马k-支配的更多结果
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-07-21 DOI: 10.1007/s00010-025-01192-3
Michael A. Henning, Lutz Volkmann
{"title":"More results on the signed double Roman k-domination in graphs","authors":"Michael A. Henning,&nbsp;Lutz Volkmann","doi":"10.1007/s00010-025-01192-3","DOIUrl":"10.1007/s00010-025-01192-3","url":null,"abstract":"<div><p>Let <span>(kge 1)</span> be an integer, and let <i>G</i> be a finite and simple graph with vertex set <i>V</i>(<i>G</i>). A signed double Roman <i>k</i>-dominating function (SDRkDF) on a graph <i>G</i> is defined in [Signed double Roman <i>k</i>-domination in graphs, Australas. J. Combin. 72 (2018), 82–105] as a function <span>(f :V(G) rightarrow {-1,1,2,3})</span> satisfying the conditions that <span>(sum _{xin N[v]}f(x)ge k)</span> for each vertex <span>(vin V(G))</span>, where <i>N</i>[<i>v</i>] is the closed neighborhood of <i>v</i>, every vertex <i>u</i> for which <span>(f(u)=-1)</span> is adjacent to at least one vertex <i>v</i> for which <span>(f(v)=3)</span> or adjacent to two vertices <i>x</i> and <i>y</i> with <span>(f(x)=f(y)=2)</span>, and every vertex <i>u</i> with <span>(f(u)=1)</span> is adjacent to vertex <i>v</i> with <span>(f(v)ge 2)</span>. The weight of an SDRkDF <i>f</i> is <span>(textrm{w}(f) = sum _{vin V(G)}f(v))</span>. The signed double Roman <i>k</i>-domination number <span>(gamma _{textrm{sdR}}^k(G))</span> of <i>G</i> is the minimum weight among all SDRkDF on <i>G</i>. In this paper we continue the study of the signed double Roman <i>k</i>-domination number of graphs, and we present new bounds on <span>(gamma _{textrm{sdR}}^k(G))</span>. In addition, we determine the signed double Roman <i>k</i>-domination number of some classes of graphs. Some of our results are extensions of well-known properties of the signed double Roman domination number, <span>(gamma _{textrm{sdR}}(G)=gamma _{textrm{sdR}}^1(G))</span>, introduced and investigated in [1, 2].</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"1903 - 1921"},"PeriodicalIF":0.7,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-025-01192-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110447","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
Extending domains in the section method 在section方法中扩展域
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-07-07 DOI: 10.1007/s00010-025-01188-z
Dan M. Dăianu
{"title":"Extending domains in the section method","authors":"Dan M. Dăianu","doi":"10.1007/s00010-025-01188-z","DOIUrl":"10.1007/s00010-025-01188-z","url":null,"abstract":"<div><p>We complete the section method with new simple and versatile techniques to solve some equations that have composite functions as solutions and to study Ulam stability and their hyperstability. We exemplify the malleability of the results obtained by solving equations of the form </p><div><div><span>$$begin{aligned} fleft( arccos left| cos ucdot cos vright| right) =fleft( uright) +fleft( vright) end{aligned}$$</span></div></div><p>on relevant real domains, then giving Ulam stability couples and control functions that induce hyperstability for these equations.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"1475 - 1490"},"PeriodicalIF":0.7,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-025-01188-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110413","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
A majorization extension of Fenchel’s and Young’s results with a control map 用控制图推广了Fenchel和Young的多数化结果
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-06-28 DOI: 10.1007/s00010-025-01186-1
Marek Niezgoda
{"title":"A majorization extension of Fenchel’s and Young’s results with a control map","authors":"Marek Niezgoda","doi":"10.1007/s00010-025-01186-1","DOIUrl":"10.1007/s00010-025-01186-1","url":null,"abstract":"<div><p>In this paper, the standard two-points Fenchel’s inequality is extended to a four-points version satisfying Sherman’s majorization condition. A corresponding extension of Young’s inequality is also shown. The problem of refining the standard Fenchel inequality is discussed.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"1955 - 1966"},"PeriodicalIF":0.7,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110476","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
Constructing Ricci vector fields on ({mathbb {R}}^2) with a diagonal metric 用对角度规在({mathbb {R}}^2)上构造Ricci向量场
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-06-26 DOI: 10.1007/s00010-025-01183-4
Adara M. Blaga
{"title":"Constructing Ricci vector fields on ({mathbb {R}}^2) with a diagonal metric","authors":"Adara M. Blaga","doi":"10.1007/s00010-025-01183-4","DOIUrl":"10.1007/s00010-025-01183-4","url":null,"abstract":"<div><p>We put into light Ricci vector fields on <span>({mathbb {R}}^2)</span> endowed with a diagonal metric.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"1809 - 1818"},"PeriodicalIF":0.7,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110549","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: Vector-valued Banach limits and the linear span property 修正：向量值Banach极限和线性张成的性质
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-06-12 DOI: 10.1007/s00010-025-01169-2
Wojciech Chojnacki
{"title":"Correction to: Vector-valued Banach limits and the linear span property","authors":"Wojciech Chojnacki","doi":"10.1007/s00010-025-01169-2","DOIUrl":"10.1007/s00010-025-01169-2","url":null,"abstract":"","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"2025 - 2025"},"PeriodicalIF":0.7,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110498","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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