We give asymptotic analysis of power series associated with lacunary partition functions. New partition theoretic interpretations of some basic hypergeometric series are offered as examples.
我们给出了与裂隙分割函数相关的幂级数的渐近分析。并举例说明了一些基本超几何级数的新的分区理论解释。
{"title":"On asymptotics for lacunary partition functions","authors":"Alexander E. Patkowski","doi":"10.1515/ms-2024-0046","DOIUrl":"https://doi.org/10.1515/ms-2024-0046","url":null,"abstract":"We give asymptotic analysis of power series associated with lacunary partition functions. New partition theoretic interpretations of some basic hypergeometric series are offered as examples.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511876","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}
In this paper, we define and study the variety of tense modal pseudocomplemented De Morgan algebras. This variety is a proper subvariety of the variety of tense tetravalent modal algebras. A tense modal pseudocomplemented De Morgan algebra is a modal pseudocomplemented De Morgan algebra endowed with two tense operators G and H satisfying additional conditions. Also, the variety of tense modal pseudocomplemented De Morgan algebras is intimately connected with some well-known varieties of De Morgan algebras with tense operators.
在本文中，我们定义并研究了时态模态伪补德摩根代数的种类。这个种类是时态四价模态代数种类的一个适当子种类。时态模态伪互补德摩根代数是一个模态伪互补德摩根代数，禀赋有满足附加条件的两个时态算子 G 和 H。此外，时态模态伪互补德摩根代数的种类与一些著名的带有时态算子的德摩根代数种类密切相关。
{"title":"A topological duality for tense modal pseudocomplemented De Morgan algebras","authors":"Gustavo Pelaitay, Maia Starobinsky","doi":"10.1515/ms-2024-0041","DOIUrl":"https://doi.org/10.1515/ms-2024-0041","url":null,"abstract":"In this paper, we define and study the variety of tense modal pseudocomplemented De Morgan algebras. This variety is a proper subvariety of the variety of tense tetravalent modal algebras. A tense modal pseudocomplemented De Morgan algebra is a modal pseudocomplemented De Morgan algebra endowed with two tense operators <jats:italic>G</jats:italic> and <jats:italic>H</jats:italic> satisfying additional conditions. Also, the variety of tense modal pseudocomplemented De Morgan algebras is intimately connected with some well-known varieties of De Morgan algebras with tense operators.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511874","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}
We consider an eigenvalue problem driven by the anisotropic (p, q)-Laplacian and with a Carathéodory reaction which is (p(z) − 1)-sublinear as x → + ∞. We look for positive solutions. We prove an existence, nonexistence and multiplicity theorem which is global in the parameter λ > 0, that is, we prove a bifurcation-type theorem which describes in an exact way the changes in the set of positive solutions as the parameter λ varies on ℝ̊+ = (0, + ∞).
{"title":"Global existence and multiplicity of positive solutions for anisotropic eigenvalue problems","authors":"Zhenhai Liu, Nikolaos S. Papageorgiou","doi":"10.1515/ms-2024-0051","DOIUrl":"https://doi.org/10.1515/ms-2024-0051","url":null,"abstract":"We consider an eigenvalue problem driven by the anisotropic (<jats:italic>p</jats:italic>, <jats:italic>q</jats:italic>)-Laplacian and with a Carathéodory reaction which is (<jats:italic>p</jats:italic>(<jats:italic>z</jats:italic>) − 1)-sublinear as <jats:italic>x</jats:italic> → + ∞. We look for positive solutions. We prove an existence, nonexistence and multiplicity theorem which is global in the parameter λ > 0, that is, we prove a bifurcation-type theorem which describes in an exact way the changes in the set of positive solutions as the parameter λ varies on ℝ̊<jats:sub>+</jats:sub> = (0, + ∞).","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511868","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}
Let 𝓟n := H*((ℝP∞)n) ≅ ℤ2[x1, x2, …, xn] be the graded polynomial algebra over ℤ2, where ℤ2 denotes the prime field of two elements. We investigate the Peterson hit problem for the polynomial algebra 𝓟n, viewed as a graded left module over the mod-2 Steenrod algebra, 𝓐. For n > 4, this problem is still unsolved, even in the case of n = 5 with the help of computers. In this article, we study the hit problem for the case n = 6 in the generic degree dr = 6(2r − 1) + 4.2r with r an arbitrary non-negative integer. By considering ℤ2 as a trivial 𝓐-module, then the hit problem is equivalent to the problem of finding a basis of ℤ2-vector space ℤ2 ⊗𝓐𝓟n. The main goal of the current article is to explicitly determine an admissible monomial basis of the ℤ2 vector space ℤ2 ⊗𝓐𝓟6 in some degrees. As an application, the behavior of the sixth Singer algebraic transfer in the degree 6(2r − 1) + 4.2r is also discussed at the end of this paper.
设𝓟 n := H *((ℝP ∞) n ) ≅ ℤ2[x 1, x 2, ..., x n ] 是在ℤ2 上的分级多项式代数，其中ℤ2 表示两个元素的素域。我们研究了多项式代数 𝓟 n 的彼得森命中问题，它被视为模 2 斯泰恩德代数 𝓐 上的分级左模块。对于 n > 4，即使在 n = 5 的情况下，这个问题在计算机的帮助下也仍未解决。在本文中，我们将研究 n = 6 情况下的命中问题，一般度数为 dr = 6(2 r - 1) + 4.2 r，其中 r 为任意非负整数。把ℤ2 看作一个微不足道的𝓐模块，那么命中问题就等价于找到ℤ2-向量空间ℤ2 ⊗𝓐𝓟 n 的一个基的问题。本文的主要目标是明确地确定ℤ2 向量空间 ℤ2 ⊗𝓐𝓟6 在某些程度上的可容许单轴基。作为应用，本文最后还讨论了第六星格代数转移在 6(2 r - 1) + 4.2 r 度中的行为。
{"title":"On the 𝓐-generators of the polynomial algebra as a module over the Steenrod algebra, I","authors":"Nguyen Khac Tin, Phan Phuong Dung, Hoang Nguyen Ly","doi":"10.1515/ms-2024-0058","DOIUrl":"https://doi.org/10.1515/ms-2024-0058","url":null,"abstract":"Let 𝓟<jats:sub> <jats:italic>n</jats:italic> </jats:sub> := <jats:italic>H</jats:italic> <jats:sup>*</jats:sup>((ℝ<jats:italic>P</jats:italic> <jats:sup>∞</jats:sup>)<jats:sup> <jats:italic>n</jats:italic> </jats:sup>) ≅ ℤ<jats:sub>2</jats:sub>[<jats:italic>x</jats:italic> <jats:sub>1</jats:sub>, <jats:italic>x</jats:italic> <jats:sub>2</jats:sub>, …, <jats:italic>x</jats:italic> <jats:sub> <jats:italic>n</jats:italic> </jats:sub>] be the graded polynomial algebra over ℤ<jats:sub>2</jats:sub>, where ℤ<jats:sub>2</jats:sub> denotes the prime field of two elements. We investigate the Peterson hit problem for the polynomial algebra 𝓟<jats:sub> <jats:italic>n</jats:italic> </jats:sub>, viewed as a graded left module over the mod-2 Steenrod algebra, 𝓐. For <jats:italic>n</jats:italic> > 4, this problem is still unsolved, even in the case of <jats:italic>n</jats:italic> = 5 with the help of computers. In this article, we study the hit problem for the case <jats:italic>n</jats:italic> = 6 in the generic degree <jats:italic>d<jats:sub>r</jats:sub> </jats:italic> = 6(2<jats:sup> <jats:italic>r</jats:italic> </jats:sup> − 1) + 4.2<jats:sup> <jats:italic>r</jats:italic> </jats:sup> with <jats:italic>r</jats:italic> an arbitrary non-negative integer. By considering ℤ<jats:sub>2</jats:sub> as a trivial 𝓐-module, then the hit problem is equivalent to the problem of finding a basis of ℤ<jats:sub>2</jats:sub>-vector space ℤ<jats:sub>2</jats:sub> ⊗<jats:sub>𝓐</jats:sub>𝓟<jats:sub> <jats:italic>n</jats:italic> </jats:sub>. The main goal of the current article is to explicitly determine an admissible monomial basis of the ℤ<jats:sub>2</jats:sub> vector space ℤ<jats:sub>2</jats:sub> ⊗<jats:sub>𝓐</jats:sub>𝓟<jats:sub>6</jats:sub> in some degrees. As an application, the behavior of the sixth Singer algebraic transfer in the degree 6(2<jats:sup> <jats:italic>r</jats:italic> </jats:sup> − 1) + 4.2<jats:sup> <jats:italic>r</jats:italic> </jats:sup> is also discussed at the end of this paper.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511869","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}
For n a power of two, we give a complete description of the cohomology algebra H*(G͠n,3; ℤ2) of the Grassmann manifold G͠n,3 of oriented 3-planes in ℝn. We do this by finding a reduced Gröbner basis for an ideal closely related to this cohomology algebra. Using this Gröbner basis we also present an additive basis for H*(G͠n,3; ℤ2).
对于 n 的 2 次幂，我们给出了对ℝ n 中定向 3 平面的格拉斯曼流形 G͠ n,3 的同调代数 H *(G͠ n,3; ℤ2)的完整描述。为此，我们要为与这个同调代数密切相关的理想找到一个还原的格氏基。利用这个格氏基，我们还提出了 H *(G͠ n,3; ℤ2)的加法基。
{"title":"Gröbner bases in the mod 2 cohomology of oriented Grassmann manifolds G͠ 2 t,3","authors":"Uroš A. Colović, Branislav I. Prvulović","doi":"10.1515/ms-2024-0015","DOIUrl":"https://doi.org/10.1515/ms-2024-0015","url":null,"abstract":"For <jats:italic>n</jats:italic> a power of two, we give a complete description of the cohomology algebra <jats:italic>H</jats:italic> <jats:sup>*</jats:sup>(<jats:italic>G͠</jats:italic> <jats:sub> <jats:italic>n</jats:italic>,3</jats:sub>; ℤ<jats:sub>2</jats:sub>) of the Grassmann manifold <jats:italic>G͠</jats:italic> <jats:sub> <jats:italic>n</jats:italic>,3</jats:sub> of oriented 3-planes in ℝ<jats:sup> <jats:italic>n</jats:italic> </jats:sup>. We do this by finding a reduced Gröbner basis for an ideal closely related to this cohomology algebra. Using this Gröbner basis we also present an additive basis for <jats:italic>H</jats:italic> <jats:sup>*</jats:sup>(<jats:italic>G͠</jats:italic> <jats:sub> <jats:italic>n</jats:italic>,3</jats:sub>; ℤ<jats:sub>2</jats:sub>).","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168455","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}
In the present paper, we prove the monotonicity property of the ratios of the generalized Volterra function. As consequences, new and interesting monotonicity concerning ratios of the exponential integral function, as well as it yields some new functional inequalities including Turán-type inequalities. Moreover, two-side bounding inequalities are then obtained for the generalized Volterra function. The main mathematical tools are some integral inequalities. As applications, a few of upper and lower bound inequalities for the exponential integral function are derived. The various results, which are established in this paper, are presumably new, and their importance is illustrated by several interesting consequences and examples accompanied by graphical representations to substantiate the accuracy of the obtained results. Some potential directions for analogous further research on the subject of the present investigation are indicated in the concluding section.
{"title":"Class of bounds of the generalized Volterra functions","authors":"Khaled Mehrez, Kamel Brahim, Sergei M. Sitnik","doi":"10.1515/ms-2024-0028","DOIUrl":"https://doi.org/10.1515/ms-2024-0028","url":null,"abstract":"In the present paper, we prove the monotonicity property of the ratios of the generalized Volterra function. As consequences, new and interesting monotonicity concerning ratios of the exponential integral function, as well as it yields some new functional inequalities including Turán-type inequalities. Moreover, two-side bounding inequalities are then obtained for the generalized Volterra function. The main mathematical tools are some integral inequalities. As applications, a few of upper and lower bound inequalities for the exponential integral function are derived. The various results, which are established in this paper, are presumably new, and their importance is illustrated by several interesting consequences and examples accompanied by graphical representations to substantiate the accuracy of the obtained results. Some potential directions for analogous further research on the subject of the present investigation are indicated in the concluding section.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168525","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}
GPE-algebras were introduced by Dvurečenskij and Vetterlein as unbounded pseudo-effect algebras. Recently, they have been characterized as partial L-algebras with local duality. In the present paper, GPE-algebras with an everywhere defined L-algebra operation are investigated. For example, linearly ordered GPE-algebra are of that type. They are characterized by their self-similar closures which are represented as negative cones of totally ordered groups. More generally, GPE-algebras with an everywhere defined multiplication are identified as negative cones of directed groups. If their partial L-algebra structure is globally defined, the enveloping group is lattice-ordered. For any self-similar L-algebra A, exponent maps are introduced, generalizing conjugation in the structure group. It is proved that the exponent maps are L-algebra automorphisms of A if and only if A is a GPE-algebra. As an application, a new characterization of cone algebras is obtained. Lattice GPE-algebras are shown to be equivalent to ∧-closed L-algebras with local duality.
GPE 对象是由 Dvurečenskij 和 Vetterlein 作为无界伪效应对象引入的。最近，它们又被表征为具有局部对偶性的部分 L 后拉。本文研究了具有无处不定义的 L 代数运算的 GPE 对象。例如，线性有序 GPE-algebra 就是这种类型。它们的特点是自相似闭包，表示为完全有序群的负锥。更一般地说，具有无处不定义的乘法的 GPE-代数被认定为有向群的负锥。如果它们的偏 L-代数结构是全局定义的，那么包络群就是网格有序的。对于任何自相似 L 代数 A，都引入了指数映射，在结构群中概括了共轭。证明了当且仅当 A 是 GPE 代数时，指数映射是 A 的 L 代数自形变。作为应用，还得到了锥体代数的新特征。网格 GPE-代数被证明等价于具有局部对偶性的 ∧ 封闭 L-代数。
{"title":"Non-commutative effect algebras, L-algebras, and local duality","authors":"Wolfgang Rump","doi":"10.1515/ms-2024-0034","DOIUrl":"https://doi.org/10.1515/ms-2024-0034","url":null,"abstract":"GPE-algebras were introduced by Dvurečenskij and Vetterlein as unbounded pseudo-effect algebras. Recently, they have been characterized as partial <jats:italic>L</jats:italic>-algebras with local duality. In the present paper, GPE-algebras with an everywhere defined <jats:italic>L</jats:italic>-algebra operation are investigated. For example, linearly ordered GPE-algebra are of that type. They are characterized by their self-similar closures which are represented as negative cones of totally ordered groups. More generally, GPE-algebras with an everywhere defined multiplication are identified as negative cones of directed groups. If their partial <jats:italic>L</jats:italic>-algebra structure is globally defined, the enveloping group is lattice-ordered. For any self-similar <jats:italic>L</jats:italic>-algebra <jats:italic>A</jats:italic>, exponent maps are introduced, generalizing conjugation in the structure group. It is proved that the exponent maps are <jats:italic>L</jats:italic>-algebra automorphisms of <jats:italic>A</jats:italic> if and only if <jats:italic>A</jats:italic> is a GPE-algebra. As an application, a new characterization of cone algebras is obtained. Lattice GPE-algebras are shown to be equivalent to ∧-closed <jats:italic>L</jats:italic>-algebras with local duality.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168538","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}
It was proved by S. Mazur and S. Ulam in 1932 that every isometric surjection between normed real vector spaces is affine. We generalize the Mazur–Ulam theorem and find necessary and sufficient conditions under which distance-preserving mappings between seminormed real vector spaces are linear.
S. Mazur 和 S. Ulam 于 1932 年证明，规范实向量空间之间的每个等距投影都是仿射。我们推广了马祖-乌拉姆定理，并找到了半规范实向量空间之间保距映射是线性的必要条件和充分条件。
{"title":"Decomposition in direct sum of seminormed vector spaces and Mazur–Ulam theorem","authors":"Oleksiy Dovgoshey, Jürgen Prestin, Igor Shevchuk","doi":"10.1515/ms-2024-0010","DOIUrl":"https://doi.org/10.1515/ms-2024-0010","url":null,"abstract":"It was proved by S. Mazur and S. Ulam in 1932 that every isometric surjection between normed real vector spaces is affine. We generalize the Mazur–Ulam theorem and find necessary and sufficient conditions under which distance-preserving mappings between seminormed real vector spaces are linear.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168635","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}
In this work we investigate a nonlocal problem for the Fredholm integro-differential equation involving integral condition. The main tool used in our considerations is Dzhumabaev parametrization method. We make use of the numerical implementation of the Dzhumabaev parametrization method to obtain the desired result, which is well-supported with numerical examples.
{"title":"Solving Fredholm integro-differential equations involving integral condition: A new numerical method","authors":"Zhazira Kadirbayeva, Elmira Bakirova, Agila Tleulessova","doi":"10.1515/ms-2024-0031","DOIUrl":"https://doi.org/10.1515/ms-2024-0031","url":null,"abstract":"In this work we investigate a nonlocal problem for the Fredholm integro-differential equation involving integral condition. The main tool used in our considerations is Dzhumabaev parametrization method. We make use of the numerical implementation of the Dzhumabaev parametrization method to obtain the desired result, which is well-supported with numerical examples.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168524","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}
In this correspondence, we prove the von Bahr–Esseen moment inequality for pairwise independent random vectors in Hilbert spaces. Our constant in the von Bahr–Esseen moment inequality is better than that obtained for the real-valued random variables by Chen et al. [The von Bahr–Esseen moment inequality for pairwise independent random variables and applications, J. Math. Anal. Appl. 419 (2014), 1290–1302], and Chen and Sung [Generalized Marcinkiewicz–Zygmund type inequalities for random variables and applications, J. Math. Inequal. 10(3) (2016), 837–848]. The result is then applied to obtain mean convergence theorems for triangular arrays of rowwise and pairwise independent random vectors in Hilbert spaces. Some results in the literature are extended.
在这篇论文中，我们证明了希尔伯特空间中成对独立随机向量的 von Bahr-Esseen 矩不等式。我们在 von Bahr-Esseen 矩不等式中的常数优于 Chen 等人在实值随机变量中得到的常数[The von Bahr-Esseen moment inequality for pairwise independent random variables and applications, J. Math. Analys.Anal.419 (2014), 1290-1302] 以及 Chen 和 Sung [Generalized Marcinkiewicz-Zygmund type inequalities for random variables and applications, J. Math. Inequal.Inequal.10(3) (2016), 837-848].然后应用该结果获得希尔伯特空间中行独立和成对独立随机向量三角阵列的均值收敛定理。文献中的一些结果得到了扩展。
{"title":"On the von Bahr–Esseen inequality for pairwise independent random vectors in Hilbert spaces with applications to mean convergence","authors":"Nguyen Chi Dzung, Nguyen Thi Thanh Hien","doi":"10.1515/ms-2024-0016","DOIUrl":"https://doi.org/10.1515/ms-2024-0016","url":null,"abstract":"In this correspondence, we prove the von Bahr–Esseen moment inequality for pairwise independent random vectors in Hilbert spaces. Our constant in the von Bahr–Esseen moment inequality is better than that obtained for the real-valued random variables by Chen et al. [<jats:italic>The von Bahr–Esseen moment inequality for pairwise independent random variables and applications</jats:italic>, J. Math. Anal. Appl. 419 (2014), 1290–1302], and Chen and Sung [<jats:italic>Generalized Marcinkiewicz–Zygmund type inequalities for random variables and applications</jats:italic>, J. Math. Inequal. 10(3) (2016), 837–848]. The result is then applied to obtain mean convergence theorems for triangular arrays of rowwise and pairwise independent random vectors in Hilbert spaces. Some results in the literature are extended.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170124","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}
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