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$$varepsilon $$ -isometries in $$l^n_1$$ $$l^n_1$$ 中的 $$varepsilon $$ 等分线
IF 0.8 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":"https://doi.org/10.1007/s00010-023-01023-3","url":null,"abstract":"<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>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"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 0.8 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, Omar Hirzallah, Fuad Kittaneh","doi":"10.1007/s00010-023-01025-1","DOIUrl":"https://doi.org/10.1007/s00010-023-01025-1","url":null,"abstract":"<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>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"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
Correction to: Regularity properties of k-Brjuno and Wilton functions 更正：k-Brjuno 和威尔顿函数的正则特性
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-01-17 DOI: 10.1007/s00010-023-01028-y
Seul Bee Lee, Stefano Marmi, Izabela Petrykiewicz, Tanja I. Schindler
{"title":"Correction to: Regularity properties of k-Brjuno and Wilton functions","authors":"Seul Bee Lee,&nbsp;Stefano Marmi,&nbsp;Izabela Petrykiewicz,&nbsp;Tanja I. Schindler","doi":"10.1007/s00010-023-01028-y","DOIUrl":"10.1007/s00010-023-01028-y","url":null,"abstract":"","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-023-01028-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140505080","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 the ({A_{!mathbb {C}}})-rank of multidigraphs 关于多图的 $${A_{!
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2023-12-26 DOI: 10.1007/s00010-023-01020-6
Sasmita Barik, Sane Umesh Reddy
{"title":"On the ({A_{!mathbb {C}}})-rank of multidigraphs","authors":"Sasmita Barik,&nbsp;Sane Umesh Reddy","doi":"10.1007/s00010-023-01020-6","DOIUrl":"10.1007/s00010-023-01020-6","url":null,"abstract":"<div><p>The complex adjacency matrix <span>({A_{!mathbb {C}}}(G))</span> for a multidigraph <i>G</i> is introduced in Barik and Sahoo (AKCE Int J Graphs Comb 17(1):466–479, 2020). We study the rank of multidigraphs corresponding to the complex adjacency matrix and call it <span>({A_{!mathbb {C}}})</span>-rank. It is known that a connected graph <i>G</i> has rank 2 if and only if <i>G</i> is a complete bipartite graph, and has rank 3 if and only if it is a complete tripartite graph (Cheng in Electron J Linear Algebra 16:60–67, 2007). We observe that these results hold as special cases for multidigraphs but are not sufficient. In this article, we characterize all multidigraphs with <span>({A_{!mathbb {C}}})</span>-rank 2 and 3, respectively.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139054274","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 the state of the second part of Hilbert’s fifth problem 关于希尔伯特第五问题第二部分的状况
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2023-12-22 DOI: 10.1007/s00010-023-01021-5
Antal Járai
{"title":"On the state of the second part of Hilbert’s fifth problem","authors":"Antal Járai","doi":"10.1007/s00010-023-01021-5","DOIUrl":"10.1007/s00010-023-01021-5","url":null,"abstract":"<div><p>In the second part of his fifth problem Hilbert asks for functional equations “In how far are the assertions which we can make in the case of differentiable functions true under proper modifications without this assumption.” In the case of the general functional equation </p><div><div><span>$$begin{aligned} f(x)=hBigl (x,y,bigl (g_1(x,y)bigr ),ldots ,bigl (g_n(x,y)bigr )Bigr ) end{aligned}$$</span></div></div><p>for the unknown function <i>f</i> under natural condition for the given functions it is proved on compact manifolds that <span>(fin C^{-1})</span> implies <span>(fin C^{infty })</span> and practically the general case can also be treated. The natural conditions imply that the dimension of <i>x</i> cannot be larger than the dimension of <i>y</i>. If we remove this condition, then we have to add another condition. In this survey paper a new problem for this second case is formulated and results are summarised for both cases.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-023-01021-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138946533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a class of functional difference equations: explicit solutions, asymptotic behavior and applications 关于一类函数差分方程：显式解法、渐近行为和应用
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2023-12-21 DOI: 10.1007/s00010-023-01022-4
Nataliya Vasylyeva
{"title":"On a class of functional difference equations: explicit solutions, asymptotic behavior and applications","authors":"Nataliya Vasylyeva","doi":"10.1007/s00010-023-01022-4","DOIUrl":"10.1007/s00010-023-01022-4","url":null,"abstract":"<div><p>For <span>(nu in [0,1])</span> and a complex parameter <span>(sigma ,)</span> <span>(Re, sigma &gt;0,)</span> we discuss a linear inhomogeneous functional difference equation with variable coefficients on a complex plane <span>(zin {{mathbb {C}}})</span>: </p><div><div><span>$$begin{aligned} (a_{1}sigma +a_{2}sigma ^{nu })mathcal {Y}(z+beta ,sigma )-Omega (z)mathcal {Y}(z,sigma )={mathbb {F}}(z,sigma ), quad beta in {mathbb {R}},, beta ne 0, end{aligned}$$</span></div></div><p>where <span>(Omega (z))</span> and <span>({mathbb {F}}(z))</span> are given complex functions, while <span>(a_{1})</span> and <span>(a_{2})</span> are given real non-negative numbers. Under suitable conditions on the given functions and parameters, we construct explicit solutions of the equation and describe their asymptotic behavior as <span>(|z|rightarrow +infty )</span>. Some applications to the theory of functional difference equations and to the theory of boundary value problems governed by subdiffusion in nonsmooth domains are then discussed.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139025508","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
Remarks on Wright-convex functions 关于赖特凸函数的评论
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2023-12-12 DOI: 10.1007/s00010-023-01024-2
Andrzej Olbryś
{"title":"Remarks on Wright-convex functions","authors":"Andrzej Olbryś","doi":"10.1007/s00010-023-01024-2","DOIUrl":"10.1007/s00010-023-01024-2","url":null,"abstract":"<div><p>In the present paper we prove a generalized version of the famous decomposition theorem of Ng. We also focus on the problem posed by Zsolt Páles concerning the Wright-convex functions.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-023-01024-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138581074","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
László Székelyhidi László Székelyhidi
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2023-12-12 DOI: 10.1007/s00010-023-01026-0
Attila Gilányi
{"title":"László Székelyhidi","authors":"Attila Gilányi","doi":"10.1007/s00010-023-01026-0","DOIUrl":"10.1007/s00010-023-01026-0","url":null,"abstract":"","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-023-01026-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139008714","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
Maciej Sablik 马切伊-萨布利克
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2023-12-11 DOI: 10.1007/s00010-023-01019-z
Roman Ger
{"title":"Maciej Sablik","authors":"Roman Ger","doi":"10.1007/s00010-023-01019-z","DOIUrl":"10.1007/s00010-023-01019-z","url":null,"abstract":"","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-023-01019-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138568165","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
Quadratic functions fulfilling an additional condition along the hyperbola (pmb {xy = 1} ) 沿双曲线满足附加条件的二次函数 $$pmb {xy = 1} $$
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2023-11-25 DOI: 10.1007/s00010-023-01018-0
Zoltán Boros, Edit Garda-Mátyás
{"title":"Quadratic functions fulfilling an additional condition along the hyperbola (pmb {xy = 1} )","authors":"Zoltán Boros,&nbsp;Edit Garda-Mátyás","doi":"10.1007/s00010-023-01018-0","DOIUrl":"10.1007/s00010-023-01018-0","url":null,"abstract":"<div><p>In this paper we give necessary conditions for quadratic functions <span>( f :mathbb {R}rightarrow mathbb {R})</span> that satisfy the additional equation <span>( y^2 f(x) = x^2 f(y) )</span> under the condition <span>( xy = 1 ,)</span>.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-023-01018-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138536259","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
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