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g-convex functions and some of their properties g-凸函数及其一些性质
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2026-08-20 DOI: 10.1007/s10474-026-01621-y
Bessem Samet
{"title":"g-convex functions and some of their properties","authors":"Bessem Samet","doi":"10.1007/s10474-026-01621-y","DOIUrl":"10.1007/s10474-026-01621-y","url":null,"abstract":"<div><p>In this work, we propose a new generalization of the notion of convexity of functions. Namely, for a function <span>(g :mathbb {R}rightarrow mathbb {R})</span>, we introduce the class of functions <span>(f :J rightarrow mathbb {R})</span> (<i>J</i> is an interval of <span>(mathbb {R})</span>) satisfying </p><div><div><span>$$ f(x)le frac{g(u_2-x)}{g(u_2-u_1)}f(u_1)+frac{g(x-u_1)}{g(u_2-u_1)}f(u_2),quad u_1le xle u_2, $$</span></div></div><p>for every subinterval <span>([u_1,u_2]subset J)</span> with <span>(u_1&lt;u_2)</span>. We call any function <i>f</i> satisfying the above property: a <i>g</i>-convex function on <i>J</i>. Clearly, any convex function on <i>J</i> is a <i>g</i>-convex function on <i>J</i>, where <span>(g(x)=x)</span>. Furthermore, the proposed class of functions includes other types of convexity from the literature for other choices of the function <i>g</i>. Some properties of <i>g</i>-convex functions are established. Next, some applications including a trapezoidal-type result are provided.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"69 - 86"},"PeriodicalIF":0.6,"publicationDate":"2026-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176508","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
Sine laws on semigroups with an involutive anti-automorphism: a Levi-Civita approach via left translations 具有对合反自同构的半群上的正弦律：通过左翻译的列维-奇维塔方法
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2026-08-19 DOI: 10.1007/s10474-026-01629-4
Đặng Võ Phúc
{"title":"Sine laws on semigroups with an involutive anti-automorphism: a Levi-Civita approach via left translations","authors":"Đặng Võ Phúc","doi":"10.1007/s10474-026-01629-4","DOIUrl":"10.1007/s10474-026-01629-4","url":null,"abstract":"<div><p>Stetkær’s matrix (Levi-Civita) method is a powerful tool for functional equations on semigroups involving a homomorphism <span>(sigma )</span>, as it yields a finite-dimensional invariant space under right translations and a corresponding matrix formalism. However, this framework collapses when <span>(sigma )</span> is an involutive anti-automorphism due to the order reversal in the right-regular action. In this paper, we overcome this obstruction at the operator level by establishing the conjugation identity: letting <i>J</i> denote composition with <span>(sigma )</span>, we prove </p><div><div><span>$$ J,R(sigma (y)),J=L(y)quad (forall ,yin S), $$</span></div></div><p>which converts the problematic right translates into left translations. Using this left-translation approach, we obtain an anti-automorphic Levi-Civita closure principle and apply it to the generalized sine law. Remarkably, the classical dichotomy <span>(beta in {pm 1})</span> and the parity relation <span>(fcirc sigma =beta f)</span> are recovered unconditionally. Furthermore, under a natural bridge hypothesis, which is automatically satisfied when there exists a central element <i>c</i> with <span>(f(c)ne 0)</span>, we obtain the corresponding standard <i>xy</i>-addition law and the exact <span>(sigma )</span>-transformation rule for <i>g</i>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"54 - 68"},"PeriodicalIF":0.6,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176728","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 an open problem about (sigma )-wideness of subgroups 关于(sigma ) -子群宽度的一个开放问题
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2026-08-18 DOI: 10.1007/s10474-026-01622-x
Zhenfeng Wu
{"title":"On an open problem about (sigma )-wideness of subgroups","authors":"Zhenfeng Wu","doi":"10.1007/s10474-026-01622-x","DOIUrl":"10.1007/s10474-026-01622-x","url":null,"abstract":"<div><p>Let <i>G</i> be a finite group and <span>(sigma ={sigma _{i}|iin I})</span> be a partition of the set of all primes <span>(mathbb {P})</span>, that is, <span>(mathbb {P}=bigcup _{iin I}sigma _{i})</span> and <span>(sigma _{i}cap sigma _{j}=emptyset )</span> for all <span>(ine j)</span>. We write <span>(sigma (n))</span> to denote the set <span>({sigma _i|sigma _icap pi (n)ne emptyset })</span>, and <span>(sigma (G)=sigma (|G|))</span>. A subgroup <i>H</i> of <i>G</i> is said to be <span>(sigma )</span>-wide if <span>(sigma (H)=sigma (G))</span>. A group <i>G</i> is called quasi-<i>k</i>-<span>(sigma )</span>-primary if <span>(|sigma (G)|&gt;k)</span> and <span>(|sigma (M)|le k)</span> for any maximal subgroup <i>M</i> of <i>G</i>. In this paper, firstly, we study the structure of a finite <span>(sigma )</span>-solvable group <i>G</i> in which every <span>(sigma )</span>-wide subgroup of <i>G</i> is <span>(sigma )</span>-nilpotent; secondly, we give a description of <span>(sigma )</span>-solvable quasi-<i>k</i>-<span>(sigma )</span>-primary group. And we also give an counterexample to answer the open problem which posed by Skiba in [12].</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"37 - 45"},"PeriodicalIF":0.6,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176819","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
Finite groups whose Schmidt subgroups are tcc-subgroups 施密特子群为tcc-子群的有限群
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2026-08-18 DOI: 10.1007/s10474-026-01626-7
Jianjun Liu, Songtai Li, Xuyang Han
{"title":"Finite groups whose Schmidt subgroups are tcc-subgroups","authors":"Jianjun Liu,&nbsp;Songtai Li,&nbsp;Xuyang Han","doi":"10.1007/s10474-026-01626-7","DOIUrl":"10.1007/s10474-026-01626-7","url":null,"abstract":"<div><p>Let <i>G</i> be a finite group. A subgroup <i>A</i> of a group <i>G</i> is called a <i>tcc</i>-subgroup of <i>G</i> if there exists a subgroup <i>B</i> of <i>G</i> such that <span>(G = AB)</span> and, for any <span>(X le A)</span> and <span>(Y le B)</span>, there is an element <span>(uin langle X, Yrangle )</span> satisfying <span>(XY^u=Y^uX)</span>. In this paper, we study the structure of a finite group <i>G</i> in which every Schmidt subgroup is a <i>tcc</i>-subgroup. Our main results show that such a group <i>G</i> is solvable. Moreover, if the Frattini subgroup <span>(Phi (G))</span> is trivial and every Schmidt subgroup is both supersolvable and a <i>tcc</i>-subgroup, then <i>G</i> itself is supersolvable.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"46 - 53"},"PeriodicalIF":0.6,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176820","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
Diophantine approximation with Piatetski-Shapiro primes 用Piatetski-Shapiro素数的丢番图近似
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2026-08-17 DOI: 10.1007/s10474-026-01620-z
Stephan Baier, Habibur Rahaman
{"title":"Diophantine approximation with Piatetski-Shapiro primes","authors":"Stephan Baier,&nbsp;Habibur Rahaman","doi":"10.1007/s10474-026-01620-z","DOIUrl":"10.1007/s10474-026-01620-z","url":null,"abstract":"<div><p>We prove that for every irrational number <span>(alpha )</span>, real number <span>(beta )</span>, real number <i>c</i> satisfying <span>(1&lt;c&lt;9/8)</span> and positive real number <span>(theta )</span> satisfying <span>(theta &lt;(9/c-8)/10)</span>, there exist infinitely many primes of the form <span>(p=left[ n^cright] )</span> with <span>(nin mathbb {N})</span> such that <span>( Vert alpha p+beta Vert &lt;p^{-theta }.)</span></p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"8 - 20"},"PeriodicalIF":0.6,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176800","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 Bowen entropy for fixed-point free flows 关于定点自由流的Bowen熵的注记
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2026-08-17 DOI: 10.1007/s10474-026-01624-9
Zhongxuan Yang, Xiaojun Huang, Shihao Meng, Jianzhong Lu
{"title":"A note on Bowen entropy for fixed-point free flows","authors":"Zhongxuan Yang,&nbsp;Xiaojun Huang,&nbsp;Shihao Meng,&nbsp;Jianzhong Lu","doi":"10.1007/s10474-026-01624-9","DOIUrl":"10.1007/s10474-026-01624-9","url":null,"abstract":"<div><p>Building on the work of Dou, Fan and Qiu, who introduced Bowen entropy for flows via reparametrization ball techniques and established a variational principle for fixed-point free flows, this paper further develops the variational principle of Bowen entropy in such systems. We introduce two new notions of measure-theoretic entropy tailored to fixed-point free flows and establish both a variational principle and an inverse variational principle relating these entropies to Bowen entropy. Finally, we give some calculations about Bowen entropy.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"21 - 36"},"PeriodicalIF":0.6,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176801","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
Locally graded groups with many (locally nilpotent)-by-Chernikov subgroups 具有许多（局部幂零的）chernikov -子群的局部分级群
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2026-07-28 DOI: 10.1007/s10474-026-01609-8
Sevgi Atlihan, Abdelhafid Badis, Amel Dilmi, Nadir Trabelsi
{"title":"Locally graded groups with many (locally nilpotent)-by-Chernikov subgroups","authors":"Sevgi Atlihan,&nbsp;Abdelhafid Badis,&nbsp;Amel Dilmi,&nbsp;Nadir Trabelsi","doi":"10.1007/s10474-026-01609-8","DOIUrl":"10.1007/s10474-026-01609-8","url":null,"abstract":"<div><p>In this work we prove that a locally graded group whose proper subgroups are (locally nilpotent)-by-Chernikov is itself (locally nilpotent)-by-Chernikov. We prove also that if <span>({varvec{G}})</span> is an <span>(mathfrak {X})</span> -group of infinite rank whose proper subgroups of infinite rank are (locally nilpotent)-by-Chernikov (respectively, Baer-by-Chernikov), then so is <span>({varvec{G}})</span>; where <span>(mathfrak {X})</span> is the class defined by N. S. Chernikov as the closure of the class of periodic locally graded groups by the closure operations <span>( varvec{acute{P}}, varvec{grave{P}})</span> and <span>( varvec{L})</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"1 - 7"},"PeriodicalIF":0.6,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176860","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
Binary quadratic forms of odd class number 奇类数的二元二次型
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2026-07-12 DOI: 10.1007/s10474-026-01614-x
Amir Akbary, Yash Totani
{"title":"Binary quadratic forms of odd class number","authors":"Amir Akbary,&nbsp;Yash Totani","doi":"10.1007/s10474-026-01614-x","DOIUrl":"10.1007/s10474-026-01614-x","url":null,"abstract":"<div><p>Let <span>(-D)</span> be a fundamental discriminant. We express the number of representations of an integer by a positive definite binary quadratic form of discriminant <span>(-D)</span> with an odd class number <span>(h(-D))</span> as a rational linear expression involving the Kronecker symbol <img> and the Fourier coefficients of certain cusp forms. We prove these cusp forms have eta quotient representations only if <span>(D=23)</span>. This provides, using theta functions, a generalization of a result of F. van der Blij from 1952 for binary quadratic forms of discriminant <span>(-23)</span> to the case of forms of discriminant <span>(-D)</span> with odd <span>(h(-D))</span>. We also classify all the eta quotients of prime level <i>D</i> which are half the difference of two theta functions of level <i>D</i>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 2","pages":"502 - 522"},"PeriodicalIF":0.6,"publicationDate":"2026-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807320","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 boundedness of the classical fractional integral operator in the variable exponent Hardy-amalgam spaces 变指数Hardy-amalgam空间中经典分数阶积分算子的有界性
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2026-07-06 DOI: 10.1007/s10474-026-01612-z
Lassane Traore, Cihan Unal
{"title":"On the boundedness of the classical fractional integral operator in the variable exponent Hardy-amalgam spaces","authors":"Lassane Traore,&nbsp;Cihan Unal","doi":"10.1007/s10474-026-01612-z","DOIUrl":"10.1007/s10474-026-01612-z","url":null,"abstract":"<div><p>In this paper, we study the mapping properties of the fractional integral operator <span>(I_{gamma })</span> <span>( (0&lt;gamma &lt;d))</span> on the Hardy-amalgam spaces with variable exponents. More precisely, we show that if the measurable exponent functions <span>(pleft( cdot right) )</span> and <i>q</i> satisfy log-Hölder continuity conditions locally and at infinity, then the fractional integral operator of order <span>(gamma )</span>, <span>(I_{gamma })</span> maps <span>(mathcal {H}^{pleft( cdot right) ,q})</span> spaces continuously into <span>(mathcal {H}^{p_{1}left( cdot right) ,q_{1}})</span> spaces on <span>(mathbb {R}^{d})</span> under the assumptions <span>(frac{1}{ p_{1}left( xright) }=frac{1}{pleft( cdot right) }-frac{gamma }{d})</span> and <span>(frac{1}{q_{1}}=frac{1}{q}-frac{gamma }{d})</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 2","pages":"486 - 501"},"PeriodicalIF":0.6,"publicationDate":"2026-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807548","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 Orlicz chord Minkowski problem Orlicz和Minkowski问题
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2026-07-06 DOI: 10.1007/s10474-026-01617-8
Min He, Wei Wang, Rigao He, Hui Zeng
{"title":"The Orlicz chord Minkowski problem","authors":"Min He,&nbsp;Wei Wang,&nbsp;Rigao He,&nbsp;Hui Zeng","doi":"10.1007/s10474-026-01617-8","DOIUrl":"10.1007/s10474-026-01617-8","url":null,"abstract":"<div><p>The existence of a solution to the Orlicz chord Minkowski problem is established under a sufficient condition, which is an extension of the <span>(L_p)</span> chord Minkowski problem for <span>(p&gt;1)</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 2","pages":"475 - 485"},"PeriodicalIF":0.6,"publicationDate":"2026-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807547","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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