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Annales Mathematicae Silesianae最新文献

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Some Existence Results for Systems of Impulsive Stochastic Differential Equations 脉冲随机微分方程组的一些存在性结果
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2021-04-13 DOI: 10.2478/amsil-2020-0028
Sliman Mekki, T. Blouhi, J. Nieto, A. Ouahab
{"title":"Some Existence Results for Systems of Impulsive Stochastic Differential Equations","authors":"Sliman Mekki, T. Blouhi, J. Nieto, A. Ouahab","doi":"10.2478/amsil-2020-0028","DOIUrl":"https://doi.org/10.2478/amsil-2020-0028","url":null,"abstract":"Abstract In this paper we study a class of impulsive systems of stochastic differential equations with infinite Brownian motions. Sufficient conditions for the existence and uniqueness of solutions are established by mean of some fixed point theorems in vector Banach spaces. An example is provided to illustrate the theory.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"35 1","pages":"260 - 281"},"PeriodicalIF":0.4,"publicationDate":"2021-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45591048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A Note on the Asymptotic Behavior of the Distribution Function of a General Sequence 关于一般序列分布函数渐近性的一个注记
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2021-01-26 DOI: 10.2478/amsil-2020-0027
Reza Farhadian, R. Jakimczuk
{"title":"A Note on the Asymptotic Behavior of the Distribution Function of a General Sequence","authors":"Reza Farhadian, R. Jakimczuk","doi":"10.2478/amsil-2020-0027","DOIUrl":"https://doi.org/10.2478/amsil-2020-0027","url":null,"abstract":"Abstract The aim of this note is to study the distribution function of certain sequences of positive integers, including, for example, Bell numbers, factorials and primorials. In fact, we establish some general asymptotic formulas in this regard. We also prove some limits that connect these sequences with the number e. Furthermore, we present a generalization of the primorial.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"35 1","pages":"44 - 54"},"PeriodicalIF":0.4,"publicationDate":"2021-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49522743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized Fractional Inequalities of the Hermite–Hadamard Type for Convex Stochastic Processes 凸随机过程的Hermite-Hadamard型广义分数不等式
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2020-12-17 DOI: 10.2478/amsil-2020-0026
M. Omaba, E. Nwaeze
{"title":"Generalized Fractional Inequalities of the Hermite–Hadamard Type for Convex Stochastic Processes","authors":"M. Omaba, E. Nwaeze","doi":"10.2478/amsil-2020-0026","DOIUrl":"https://doi.org/10.2478/amsil-2020-0026","url":null,"abstract":"Abstract A generalization of the Hermite–Hadamard (HH) inequality for a positive convex stochastic process, by means of a newly proposed fractional integral operator, is hereby established. Results involving the Riemann– Liouville, Hadamard, Erdélyi–Kober, Katugampola, Weyl and Liouville fractional integrals are deduced as particular cases of our main result. In addition, we also apply some known HH results to obtain some estimates for the expectations of integrals of convex and p-convex stochastic processes. As a side note, we also pointed out a mistake in the main result of the paper [Hermite–Hadamard type inequalities, convex stochastic processes and Katugampola fractional integral, Revista Integración, temas de matemáticas 36 (2018), no. 2, 133–149]. We anticipate that the idea employed herein will inspire further research in this direction.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"35 1","pages":"90 - 104"},"PeriodicalIF":0.4,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47156867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Thermodynamic Formalism Methods In the Theory of Iteration of Mappings in Dimension One, Real and Complex 一维映射迭代理论中的热力学形式化方法，实数与复数
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2020-12-14 DOI: 10.2478/amsil-2020-0023
F. Przytycki
{"title":"Thermodynamic Formalism Methods In the Theory of Iteration of Mappings in Dimension One, Real and Complex","authors":"F. Przytycki","doi":"10.2478/amsil-2020-0023","DOIUrl":"https://doi.org/10.2478/amsil-2020-0023","url":null,"abstract":"Received: 10.09.2020.Accepted: 08.11.2020. (2020) Mathematics Subject Classification: 37D35, 37E05, 37F10, 37F35, 31A20.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"50 6","pages":"1 - 20"},"PeriodicalIF":0.4,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41259273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Variant of D’alembert’s Matrix Functional Equation 达朗贝尔矩阵泛函方程的一种变体
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2020-12-14 DOI: 10.2478/amsil-2020-0025
Y. Aissi, D. Zeglami, M. Ayoubi
{"title":"A Variant of D’alembert’s Matrix Functional Equation","authors":"Y. Aissi, D. Zeglami, M. Ayoubi","doi":"10.2478/amsil-2020-0025","DOIUrl":"https://doi.org/10.2478/amsil-2020-0025","url":null,"abstract":"Abstract The aim of this paper is to characterize the solutions Φ : G → M2(ℂ) of the following matrix functional equations Φ(xy)+Φ(σ(y)x)2=Φ(x)Φ(y),      x,y,∈G,{{Phi left( {xy} right) + Phi left( {sigma left( y right)x} right)} over 2} = Phi left( x right)Phi left( y right),,,,,,,x,y, in G, and Φ(xy)−Φ(σ(y)x)2=Φ(x)Φ(y),      x,y,∈G,{{Phi left( {xy} right) - Phi left( {sigma left( y right)x} right)} over 2} = Phi left( x right)Phi left( y right),,,,,,,x,y, in G, where G is a group that need not be abelian, and σ : G → G is an involutive automorphism of G. Our considerations are inspired by the papers [13, 14] in which the continuous solutions of the first equation on abelian topological groups were determined.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"35 1","pages":"21 - 43"},"PeriodicalIF":0.4,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48067494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Summing a Family of Generalized Pell Numbers 一类广义Pell数的求和
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2020-10-27 DOI: 10.2478/amsil-2020-0024
H. Prodinger
{"title":"Summing a Family of Generalized Pell Numbers","authors":"H. Prodinger","doi":"10.2478/amsil-2020-0024","DOIUrl":"https://doi.org/10.2478/amsil-2020-0024","url":null,"abstract":"Abstract A new family of generalized Pell numbers was recently introduced and studied by Bród ([2]). These numbers possess, as Fibonacci numbers, a Binet formula. Using this, partial sums of arbitrary powers of generalized Pell numbers can be summed explicitly. For this, as a first step, a power P𝓁n is expressed as a linear combination of Pmn. The summation of such expressions is then manageable using generating functions. Since the new family contains a parameter R = 2r, the relevant manipulations are quite involved, and computer algebra produced huge expressions that where not trivial to handle at times.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"35 1","pages":"105 - 112"},"PeriodicalIF":0.4,"publicationDate":"2020-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45159195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Families of Commuting Formal Power Series and Formal Functional Equations 交换形式幂级数与形式泛函方程族
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2020-10-06 DOI: 10.2478/amsil-2020-0020
H. Fripertinger, L. Reich
{"title":"Families of Commuting Formal Power Series and Formal Functional Equations","authors":"H. Fripertinger, L. Reich","doi":"10.2478/amsil-2020-0020","DOIUrl":"https://doi.org/10.2478/amsil-2020-0020","url":null,"abstract":"Abstract In this paper we describe families of commuting invertible formal power series in one indeterminate over ℂ, using the method of formal functional equations. We give a characterization of such families where the set of multipliers (first coefficients) σ of its members F (x) = σx + . . . is infinite, in particular of such families which are maximal with respect to inclusion, so called families of type I. The description of these families is based on Aczél–Jabotinsky differential equations, iteration groups, and on some results on normal forms of invertible series with respect to conjugation.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"35 1","pages":"55 - 76"},"PeriodicalIF":0.4,"publicationDate":"2020-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43964262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized Tetranacci Hybrid Numbers 广义Tetranacci混合数
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2020-10-06 DOI: 10.2478/amsil-2020-0021
Y. Soykan, E. Taşdemir
{"title":"Generalized Tetranacci Hybrid Numbers","authors":"Y. Soykan, E. Taşdemir","doi":"10.2478/amsil-2020-0021","DOIUrl":"https://doi.org/10.2478/amsil-2020-0021","url":null,"abstract":"Abstract In this paper, we introduce the generalized Tetranacci hybrid numbers and, as special cases, Tetranacci and Tetranacci-Lucas hybrid numbers. Moreover, we present Binet’s formulas, generating functions, and the summation formulas for those hybrid numbers.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"35 1","pages":"113 - 130"},"PeriodicalIF":0.4,"publicationDate":"2020-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43677978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
On the Radon-Nikodym Property for Vector Measures and Extensions of Transfunctions 泛函数向量测度与扩展的Radon-Nikodym性质
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2020-10-06 DOI: 10.2478/amsil-2020-0022
P. Mikusinski, J. P. Ward
{"title":"On the Radon-Nikodym Property for Vector Measures and Extensions of Transfunctions","authors":"P. Mikusinski, J. P. Ward","doi":"10.2478/amsil-2020-0022","DOIUrl":"https://doi.org/10.2478/amsil-2020-0022","url":null,"abstract":"Abstract If (μn)n=1∞left( {{mu _n}} right)_{n = 1}^infty are positive measures on a measurable space (X, Σ) and (vn)n=1∞left( {{v_n}} right)_{n = 1}^infty are elements of a Banach space 𝔼 such that ∑n=1∞‖vn‖μn(X)<∞sumnolimits_{n = 1}^infty {left| {{v_n}} right|{mu _n}left( X right)} < infty, then ω(S)=∑n=1∞vnμn(S)omega left( S right) = sumnolimits_{n = 1}^infty {{v_n}{mu _n}left( S right)} defines a vector measure of bounded variation on (X, Σ). We show 𝔼 has the Radon-Nikodym property if and only if every 𝔼-valued measure of bounded variation on (X, Σ) is of this form. This characterization of the Radon-Nikodym property leads to a new proof of the Lewis-Stegall theorem. We also use this result to show that under natural conditions an operator defined on positive measures has a unique extension to an operator defined on 𝔼-valued measures for any Banach space 𝔼 that has the Radon-Nikodym property.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"35 1","pages":"77 - 89"},"PeriodicalIF":0.4,"publicationDate":"2020-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46618177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
An Extension of the Abel–Liouville Identity Abel–Liouville恒等式的一个推广
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2020-09-03 DOI: 10.2478/amsil-2022-0007
Zsolt P'ales, A. Zakaria
{"title":"An Extension of the Abel–Liouville Identity","authors":"Zsolt P'ales, A. Zakaria","doi":"10.2478/amsil-2022-0007","DOIUrl":"https://doi.org/10.2478/amsil-2022-0007","url":null,"abstract":"Abstract In this note, we present an extension of the celebrated Abel– Liouville identity in terms of noncommutative complete Bell polynomials for generalized Wronskians. We also characterize the range equivalence of n-dimensional vector-valued functions in the subclass of n-times differentiable functions with a nonvanishing Wronskian.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"206 - 214"},"PeriodicalIF":0.4,"publicationDate":"2020-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41728543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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