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Carpathian Journal of Mathematics最新文献

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"Admissibility and Polynomial Dichotomy of Discrete Nonautonomous Systems" 离散非自治系统的容许性与多项式二分法
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-26 DOI: 10.37193/cjm.2022.03.18
D. Dragičević, A. L. Sasu, B. Sasu
{"title":"\"Admissibility and Polynomial Dichotomy of Discrete Nonautonomous Systems\"","authors":"D. Dragičević, A. L. Sasu, B. Sasu","doi":"10.37193/cjm.2022.03.18","DOIUrl":"https://doi.org/10.37193/cjm.2022.03.18","url":null,"abstract":"\"We give new admissibility criteria for dichotomic behaviours of discrete nonautonomous sys- tems, in infinite dimensional spaces. First, we present admissibility conditions for uniform and exponential dichotomy. Next, our study is focused on polynomial dichotomy, providing new characterizations for this no- tion by means of some double admissibilities. We obtain two categories of criteria for polynomial dichotomy, based on input-output conditions imposed to some suitable systems such that, for each one, the input sequences belong to certain $l^p$ -spaces and the outputs are bounded. We point out the importance of the assumptions re- garding the complementarity of the stable subspaces at the initial time and we also discuss the relevance of the concept of solvability (unique or not) in the admissibility criteria for polynomial dichotomies on the half-line. All the results are obtained in the general case, without any additional hypotheses on the systems coefficients and without assuming any growth type properties for the associated propagators. Furthermore, as an applica- tion of the admissibility results we establish a robustness property of the polynomial dichotomy under small perturbations\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42319542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 4
"General analytical solution of fractional Klein–Gordon equation in a spherical domain" “球面域中分数阶克莱因-戈登方程的一般解析解”
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-26 DOI: 10.37193/cjm.2022.03.16
C. Fetecau, D. Vieru
{"title":"\"General analytical solution of fractional Klein–Gordon equation in a spherical domain\"","authors":"C. Fetecau, D. Vieru","doi":"10.37193/cjm.2022.03.16","DOIUrl":"https://doi.org/10.37193/cjm.2022.03.16","url":null,"abstract":"\"Time-fractional Klein–Gordon equation in a sphere is considered for the case of central sym- metry under the time-variable Dirichlet condition. The time-fractional derivative with the power-law kernel is used. The Laplace transform and convenient transformations of the independent variable and unknown func- tion are used to determine the general analytical solution of the problem in the Laplace domain. In order to obtain the solution in the real domain, the inverse Laplace transforms of two functions of exponential type whose expressions are new in the literature have been determined. The similar solution for ordinary Klein– Gordon equation is a limiting case of general solution but a simpler form for this solution is provided. The convergence of general solution to the ordinary solution and the effects of fractional parameter on this solution are graphically underlined.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46337019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
"Lyapunov Conditions for One-Sided Discrete-Time Random Dynamical Systems" “单侧离散时间随机动力系统的李雅普诺夫条件”
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-26 DOI: 10.37193/cjm.2022.03.21
L. Biris, T. Ceausu, I. Popa, "NICOLAE MARIAN" Seimeanu
{"title":"\"Lyapunov Conditions for One-Sided Discrete-Time Random Dynamical Systems\"","authors":"L. Biris, T. Ceausu, I. Popa, \"NICOLAE MARIAN\" Seimeanu","doi":"10.37193/cjm.2022.03.21","DOIUrl":"https://doi.org/10.37193/cjm.2022.03.21","url":null,"abstract":"\"This paper considers nonuniform exponential stability and nonuniform exponential instability concepts for one-sided discrete-time random dynamical systems. These concepts are generalizations from the deterministic case. Using this, characterizations in terms of Lyapunov functions respectively Lyapunov norms are presented. Also, an approach in terms of considered concepts for the inverse and adjoint random discrete- time systems is derived.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45665635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 uniform polynomial trichotomy of skew-evolution semiflows 关于偏斜演化半流的一致多项式三分法
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-26 DOI: 10.37193/cjm.2022.03.24
C. Mihiţ
{"title":"On uniform polynomial trichotomy of skew-evolution semiflows","authors":"C. Mihiţ","doi":"10.37193/cjm.2022.03.24","DOIUrl":"https://doi.org/10.37193/cjm.2022.03.24","url":null,"abstract":"\"The paper treats two concepts of uniform polynomial trichotomy for the skew-evolution semi- flows in Banach spaces. We obtain the connection between them, a characterization for a property of uniform polynomial growth and a sufficient criteria for the uniform polynomial trichotomy.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43463763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
"Periodic solutions for certain Hamiltonian systems in arbitrary dimension and global parametrization of some manifolds" 任意维Hamiltonian系统的周期解和某些流形的全局参数化
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-26 DOI: 10.37193/cjm.2022.03.09
D. Tiba
{"title":"\"Periodic solutions for certain Hamiltonian systems in arbitrary dimension and global parametrization of some manifolds\"","authors":"D. Tiba","doi":"10.37193/cjm.2022.03.09","DOIUrl":"https://doi.org/10.37193/cjm.2022.03.09","url":null,"abstract":"\"t has been recently shown that the limit cycle situation is not valid for Hamiltonian systems in dimension two, under appropriate conditions. The applications concern global parametrizations of closed curves in the plane and optimal design problems. Here, we discuss a partial extension of this result, for certain Hamiltonian-type systems in higher dimension.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47098181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 linear quadratic tracking problem for stochastic systems controlled by impulses. The finite horizon time case 脉冲控制随机系统的线性二次跟踪问题。有限视界时间的情况
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-26 DOI: 10.37193/cjm.2022.03.17
V. Drăgan, I. Popa, I. Ivanov
{"title":"A linear quadratic tracking problem for stochastic systems controlled by impulses. The finite horizon time case","authors":"V. Drăgan, I. Popa, I. Ivanov","doi":"10.37193/cjm.2022.03.17","DOIUrl":"https://doi.org/10.37193/cjm.2022.03.17","url":null,"abstract":"\"We investigate a problem to solve the linear quadratic tracking problem for stochastic systems controlled by impulses. Two optimal control problems are investigated where the different objective functions are minimized. Explicit formulae for optimal controls are developed. The optimal controllers are computed based on the solution of the backward jump matrix Lyapunov type linear differential equations.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49174255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 early developments in fixed point theory on b-metric spaces: a brief survey and some important related aspects" b-度量空间不动点理论的早期发展:简述及有关的一些重要方面
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-26 DOI: 10.37193/cjm.2022.03.01
V. Berinde, M. Pacurar
{"title":"\"The early developments in fixed point theory on b-metric spaces: a brief survey and some important related aspects\"","authors":"V. Berinde, M. Pacurar","doi":"10.37193/cjm.2022.03.01","DOIUrl":"https://doi.org/10.37193/cjm.2022.03.01","url":null,"abstract":"\"A very impressive research work has been devoted in the last two decades to obtaining fixed point theorems in quasimetric spaces (also called b-metric spaces). Some incorrect and incomplete references with respect to the early developments on fixed point theory in b-metric spaces are though perpetually taking over from the existing publications to the new ones. Starting from this fact, our main aim in this note is threefold: (1) to briefly survey the early developments in the fixed point theory on quasimetric spaces (b-metric spaces); (2) to collect some relevant bibliography related to this topic; (3) to discuss some other aspects of current interest in the fixed point theory on quasimetric spaces (b-metric spaces).\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45709736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 11
"Hyers-Ulam stability of hom-derivations in Banach algebras" Banach代数中同导的Hyers-Ulam稳定性
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-26 DOI: 10.37193/cjm.2022.03.26
T. Mouktonglang, R. Suparatulatorn, Choonkill Park
{"title":"\"Hyers-Ulam stability of hom-derivations in Banach algebras\"","authors":"T. Mouktonglang, R. Suparatulatorn, Choonkill Park","doi":"10.37193/cjm.2022.03.26","DOIUrl":"https://doi.org/10.37193/cjm.2022.03.26","url":null,"abstract":"\"In this work, we prove the Hyers–Ulam stability of hom-derivations in complex Banach algebras, associated with the additive $(s_{1}, s_{2})$-functional inequality: begin{eqnarray}label{0.1} nonumber | f(a+b) - f(a) - f(b)| &le& left |s_{1} left(f(a+b) + f(a-b)-2f(a)right)right| &quad& + left |s_{2} left(2fleft( frac{a+b}{2}right) - f(a) - f(b)right)right|, end{eqnarray} where $s_{1}$ and $s_{2}$ are fixed nonzero complex numbers with $sqrt{2}|s_{1}|+|s_{2}| < 1$.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42129801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
"Iterates of multidimensional approximation operators via Perov theorem" “用Perov定理求解多维逼近算子的迭代”
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-26 DOI: 10.37193/cjm.2022.03.02
O. Agratini, R. Precup
{"title":"\"Iterates of multidimensional approximation operators via Perov theorem\"","authors":"O. Agratini, R. Precup","doi":"10.37193/cjm.2022.03.02","DOIUrl":"https://doi.org/10.37193/cjm.2022.03.02","url":null,"abstract":"\"The starting point is an approximation process consisting of linear and positive operators. The purpose of this note is to establish the limit of the iterates of some multidimensional approximation operators. The main tool is a Perov’s result which represents a generalization of Banach fixed point theorem. In order to support the theoretical aspects, we present three applications targeting respectively the operators Bernstein, Cheney-Sharma and those of binomial type. The last class involves an incursion into umbral calculus\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42827277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
Common fixed point theory for a pair of multivalued operators 一对多值算子的公共不动点理论
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2022-07-26 DOI: 10.37193/cjm.2022.03.15
A. Petruşel, G. Petruşel
{"title":"Common fixed point theory for a pair of multivalued operators","authors":"A. Petruşel, G. Petruşel","doi":"10.37193/cjm.2022.03.15","DOIUrl":"https://doi.org/10.37193/cjm.2022.03.15","url":null,"abstract":"\"The aim of this paper is to present a common fixed point theory for a pair of multivalued op- erators in complete metric spaces. Existence and stability results for the common fixed point problem will be discussed. The approach is based on some fixed point results for multivalued graphical contractions and for multivalued operators of Feng-Liu type. Our results extend to the multivalued case some recent results in the literature.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45822046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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