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Some moduli related to (rho _{pm })-orthogonalities and semi-orthogonality in Banach spaces Banach空间中与(rho _{pm }) -正交和半正交有关的几个模
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-20 DOI: 10.1007/s00010-025-01153-w
Dandan Du, Yongjin Li
{"title":"Some moduli related to (rho _{pm })-orthogonalities and semi-orthogonality in Banach spaces","authors":"Dandan Du,&nbsp;Yongjin Li","doi":"10.1007/s00010-025-01153-w","DOIUrl":"10.1007/s00010-025-01153-w","url":null,"abstract":"<div><p>In this article, we introduce several new moduli of convexity connected with <span>(rho _{pm })</span>-orthogonalities and semi-orthogonality, which are closely related to the modulus of convexity <span>(delta _{X}(varepsilon ))</span>. In particular, these new parameters are computed for <i>X</i> being some specific spaces. Moreover, we give some applications of these two coefficients <span>(delta _{perp }(rho _{pm }, X))</span> and investigate the relation between these two parameters and the approximate symmetry of <span>(rho _{-})</span>-orthogonality. In the meantime, we give characterization of the Radon plane with an affine-hexagonal unit sphere in terms of these new moduli of convexity. Moreover, we also consider the moduli of smoothness related to <span>(rho _{pm })</span>-orthgonalities and semi-orthogonality. In the end, we discuss some applications of these new moduli of smoothness and study some relationships between these new parameters and uniform non-squareness, uniform convexity.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"905 - 926"},"PeriodicalIF":0.9,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144074171","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
Vector-valued Banach limits and the linear span property 向量值Banach极限与线性张成的性质
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-19 DOI: 10.1007/s00010-024-01140-7
Wojciech Chojnacki
{"title":"Vector-valued Banach limits and the linear span property","authors":"Wojciech Chojnacki","doi":"10.1007/s00010-024-01140-7","DOIUrl":"10.1007/s00010-024-01140-7","url":null,"abstract":"<div><p>This paper explores the connections between vector-valued Banach limits and weak compactness in Banach spaces. We show that a Banach space, <span>({X})</span>, is reflexive if it admits a Banach limit on bounded <span>({X})</span>-valued sequences such that, for any input sequence, the corresponding limit vector lies in the closed linear span of that sequence. This conclusion is based on proving that the existence of a vector-valued Banach limit with the aforementioned linear span property implies the weak compactness of the closed unit ball of the underlying Banach space. Furthermore, we extend the above result by establishing a characterisation of the relative weak compactness of bounded sets in Banach spaces. The characterisation states that a bounded set is relatively weakly compact if, for every sequence in the set, there exists a vector-valued Banach limit on the smallest shift-invariant linear space containing the sequence and all vector-valued constant sequences, such that, for any input sequence, the corresponding limit vector lies in the closed linear span of that sequence.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"1657 - 1674"},"PeriodicalIF":0.7,"publicationDate":"2025-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167152","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
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-19
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引用次数: 0
Sorting 1-away permutations with underlying Fibonacci convolutions 用潜在的斐波那契卷积排序1-差排列
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-19 DOI: 10.1007/s00010-024-01146-1
Hosam Mahmoud
{"title":"Sorting 1-away permutations with underlying Fibonacci convolutions","authors":"Hosam Mahmoud","doi":"10.1007/s00010-024-01146-1","DOIUrl":"10.1007/s00010-024-01146-1","url":null,"abstract":"<div><p>We discuss some combinatorics associated with 1-away permutations, where an element can be displaced from its correct position by at most one location. Specifically, we look at a sorting algorithm for such permutations and analyze its number of comparisons, <span>(C_n)</span>. We find that the mean is a certain combination of two-fold convolutions of Fibonacci numbers and the variance is a certain combination of three-fold convolutions of Fibonacci numbers, with corresponding asymptotics (as <span>(nrightarrow infty )</span>): </p><div><div><span>$${mathbb {E}}[C_n] sim frac{5 + sqrt{5}}{10}, n, qquad {mathbb {V}textrm{ar}}[C_n]sim frac{sqrt{5}}{25} , n.$$</span></div></div><p>The proofs contain finer asymptotics down to exponentially small error terms. The relatively small variance admits a weak law and a central limit theorem via a super moment generating function. In view of the special nature of the data, such a specialized algorithm outperforms general comparison-based sorting algorithms.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"1209 - 1219"},"PeriodicalIF":0.9,"publicationDate":"2025-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01146-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073662","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
Symmetric probabilistic divergence generator 对称概率散度发生器
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-15 DOI: 10.1007/s00010-024-01148-z
Shounak Roychowdhury
{"title":"Symmetric probabilistic divergence generator","authors":"Shounak Roychowdhury","doi":"10.1007/s00010-024-01148-z","DOIUrl":"10.1007/s00010-024-01148-z","url":null,"abstract":"<div><p>Probabilistic divergence measures the statistical distance between two probability distributions. Traditionally, they are used in probability theory and information theory. Nowadays, many machine learning algorithms rely on such divergences to learn models and distributions of parameters, enabling them to perform a wide range of automated tasks. This small article proposes a new family of symmetric probabilistic divergences generated using a novel functional generator. The generator uses monotonically increasing and decreasing functions to create a variety of probabilistic divergences. While it is possible to generate a variety of probabilistic divergences based on the suitable choices of functions, here the focus on six new probabilistic divergences.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"1725 - 1739"},"PeriodicalIF":0.7,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165137","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
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-15
{"title":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"1725 - 1739"},"PeriodicalIF":0.7,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110592","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: On the solvability of the (SSIE) with operator ({D}_{x} {mathbf { * }}left( { s}_{ R}^{{textbf{0}}} right) _{{{{Sigma }} - {lambda I}}} {{ subset }}{ s}_{ R}^{{{0}}} ), involving the fine spectrum of an operator 修正：关于（SSIE）与算子({D}_{x} {mathbf { * }}left( { s}_{ R}^{{textbf{0}}} right) _{{{{Sigma }} - {lambda I}}} {{ subset }}{ s}_{ R}^{{{0}}} )的可解性，涉及算子的精细谱
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-15 DOI: 10.1007/s00010-024-01142-5
Bruno de Malafosse, Eberhard Malkowsky, Vladinir Rakočević
{"title":"Correction to: On the solvability of the (SSIE) with operator ({D}_{x} {mathbf { * }}left( { s}_{ R}^{{textbf{0}}} right) _{{{{Sigma }} - {lambda I}}} {{ subset }}{ s}_{ R}^{{{0}}} ), involving the fine spectrum of an operator","authors":"Bruno de Malafosse,&nbsp;Eberhard Malkowsky,&nbsp;Vladinir Rakočević","doi":"10.1007/s00010-024-01142-5","DOIUrl":"10.1007/s00010-024-01142-5","url":null,"abstract":"","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 2","pages":"823 - 824"},"PeriodicalIF":0.9,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143871356","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
d-Young distance function and existence of fixed points in complete metric spaces 完备度量空间中d-Young距离函数与不动点的存在性
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-13 DOI: 10.1007/s00010-024-01144-3
Vladimir Rakočević, Bessem Samet
{"title":"d-Young distance function and existence of fixed points in complete metric spaces","authors":"Vladimir Rakočević,&nbsp;Bessem Samet","doi":"10.1007/s00010-024-01144-3","DOIUrl":"10.1007/s00010-024-01144-3","url":null,"abstract":"<div><p>We introduce the concept of <i>d</i>-Young distance function with respect to the 5-uplet <span>((p,q,tau ,kappa ,xi ))</span>, where <i>d</i> is a metric on a certain set <span>(Lambda )</span>, <span>(1&lt;p,q&lt;infty )</span> with <span>(frac{1}{p}+frac{1}{q}=1)</span>, <span>(tau : Lambda times Lambda rightarrow [0,infty ))</span>, <span>(kappa &gt;0)</span>, and <span>(xi : [0,infty )rightarrow [0,infty ))</span> satisfies the condition <span>(inf _{t&gt;0} frac{xi (t)}{t^kappa }&gt;0)</span>. We establish some properties of the introduced distance function. Next, we study the existence and uniqueness of fixed points for some classes of mappings <span>(F: Lambda rightarrow Lambda )</span> satisfying contractions involving the <i>d</i>-Young distance function. In particular, for a special choice of the 5-uplet <span>((p,q,tau ,kappa ,xi ))</span>, we recover the Banach fixed point theorem. We also provide an example, where our approach can be used, but the Banach fixed point theorem is inapplicable.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"1625 - 1639"},"PeriodicalIF":0.7,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110554","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
Levin–Cochran–Lee inequalities and best constants on homogeneous groups 齐次群上的Levin-Cochran-Lee不等式和最佳常数
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-13 DOI: 10.1007/s00010-024-01143-4
Michael Ruzhansky, Markos Fisseha Yimer
{"title":"Levin–Cochran–Lee inequalities and best constants on homogeneous groups","authors":"Michael Ruzhansky,&nbsp;Markos Fisseha Yimer","doi":"10.1007/s00010-024-01143-4","DOIUrl":"10.1007/s00010-024-01143-4","url":null,"abstract":"<div><p>In this paper, we apply a direct method instead of a limit approach, for proving the Levin–Cochran–Lee inequalities. First, we state and prove Levin–Cochran–Lee type inequalities on a homogeneous group <span>(mathbb {G})</span> with parameters <span>(0&lt;ple q&lt;infty )</span>. Furthermore, for the case <span>(p=q)</span>, we prove the sharp inequalities with power weights and derive some other new inequalities.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"1603 - 1623"},"PeriodicalIF":0.7,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110500","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
Congruence properties of Lehmer-Euler numbers Lehmer-Euler数的同余性质
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-10 DOI: 10.1007/s00010-024-01150-5
Takao Komatsu, Guo-Dong Liu
{"title":"Congruence properties of Lehmer-Euler numbers","authors":"Takao Komatsu,&nbsp;Guo-Dong Liu","doi":"10.1007/s00010-024-01150-5","DOIUrl":"10.1007/s00010-024-01150-5","url":null,"abstract":"<div><p>Certain generalization of Euler numbers was defined in 1935 by Lehmer using cubic roots of unity, as a natural generalization of Bernoulli and Euler numbers. In this paper, Lehmer’s generalized Euler numbers are studied to give certain congruence properties together with recurrence and explicit formulas of the numbers. We also show a new polynomial sequence and its properties. Some identities including Euler and central factorial numbers are obtained.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"1337 - 1355"},"PeriodicalIF":0.9,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144074048","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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