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Banach-Steinhaus theorem for linear relations on asymmetric normed spaces 非对称赋范空间上线性关系的Banach-Steinhaus定理
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-06-30 DOI: 10.15330/cmp.14.1.230-237
K. Bouadjila, A. Tallab, E. Dahia
{"title":"Banach-Steinhaus theorem for linear relations on asymmetric normed spaces","authors":"K. Bouadjila, A. Tallab, E. Dahia","doi":"10.15330/cmp.14.1.230-237","DOIUrl":"https://doi.org/10.15330/cmp.14.1.230-237","url":null,"abstract":"We study the continuity of linear relations defined on asymmetric normed spaces with values in normed spaces. We give some geometric charactirization of these mappings. As an application, we prove the Banach-Steinhaus theorem in the framework of asymmetric normed spaces.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91139082","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
On approximation of functions from the class $L^{psi}_{beta, 1}$ by the Abel-Poisson integrals in the integral metric 用积分度规中的Abel-Poisson积分逼近$L^{psi}_{beta, 1}$类函数
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-06-30 DOI: 10.15330/cmp.14.1.223-229
T. V. Zhyhallo, Yu. I. Kharkevych
{"title":"On approximation of functions from the class $L^{psi}_{beta, 1}$ by the Abel-Poisson integrals in the integral metric","authors":"T. V. Zhyhallo, Yu. I. Kharkevych","doi":"10.15330/cmp.14.1.223-229","DOIUrl":"https://doi.org/10.15330/cmp.14.1.223-229","url":null,"abstract":"In the paper, we investigate an asymptotic behavior of the sharp upper bounds in the integral metric of deviations of the Abel-Poisson integrals from functions from the class $L^{psi}_{beta, 1}$. The Abel-Poisson integrals are solutions of the partial differential equations of elliptic type with corresponding boundary conditions, and they play an important role in applied problems. The approximative properties of the Abel-Poisson integrals on different classes of differentiable functions were studied in a number of papers. Nevertheless, a problem on the respective approximation on the classes $L^{psi}_{beta,1}$ in the metric of the space $L$ remained unsolved. We managed to obtain the estimates for the values of approximation of $(psi, beta)$-differentiable functions from the unit ball of the space $L$ by the Abel-Poisson integrals. In some cases, we also write down asymptotic equalities for these quantities, that is we solve the Kolmogorov-Nikol'skii problem for the the Abel-Poisson integrals on the classes $L^{psi}_{beta,1}$ in the integral metric.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72492515","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: 23
Torsion locally nilpotent groups with non-Dedekind norm of Abelian non-cyclic subgroups Abelian非循环子群的非dedekind范数的扭转局部幂零群
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-06-30 DOI: 10.15330/cmp.14.1.247-259
T. Lukashova, M. Drushlyak
{"title":"Torsion locally nilpotent groups with non-Dedekind norm of Abelian non-cyclic subgroups","authors":"T. Lukashova, M. Drushlyak","doi":"10.15330/cmp.14.1.247-259","DOIUrl":"https://doi.org/10.15330/cmp.14.1.247-259","url":null,"abstract":"The authors study relations between the properties of torsion locally nilpotent groups and their norms of Abelian non-cyclic subgroups. The impact of the norm of Abelian non-cyclic subgroups on the properties of the group under the condition of norm non-Dedekindness is investigated. It was found that for these restrictions, torsion locally nilpotent groups are finite extensions of a quasi-cyclic subgroup and the structure of such groups is completely described.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78336884","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
On families of twisted power partial isometries 关于扭转幂部分等距的族
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-06-30 DOI: 10.15330/cmp.14.1.260-265
V. Ostrovskyi, D. Proskurin, R. Yakymiv
{"title":"On families of twisted power partial isometries","authors":"V. Ostrovskyi, D. Proskurin, R. Yakymiv","doi":"10.15330/cmp.14.1.260-265","DOIUrl":"https://doi.org/10.15330/cmp.14.1.260-265","url":null,"abstract":"We consider families of power partial isometries satisfying twisted commutation relations with deformation parameters $lambda_{ij}inmathbb C$, $|lambda_{ij}|=1$. Irreducible representations of such a families are described up to the unitary equivalence. Namely any such representation corresponds, up to the unitary equivalence, to irreducible representation of certain higher-dimensional non-commutative torus.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89248212","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
On Wick calculus and its relationship with stochastic integration on spaces of regular test functions in the Lévy white noise analysis l<s:1>白噪声分析中Wick微积分及其与正则测试函数空间上随机积分的关系
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-06-23 DOI: 10.15330/cmp.14.1.194-212
N. A. Kachanovsky
{"title":"On Wick calculus and its relationship with stochastic integration on spaces of regular test functions in the Lévy white noise analysis","authors":"N. A. Kachanovsky","doi":"10.15330/cmp.14.1.194-212","DOIUrl":"https://doi.org/10.15330/cmp.14.1.194-212","url":null,"abstract":"We deal with spaces of regular test functions in the Lévy white noise analysis, which are constructed using Lytvynov's generalization of a chaotic representation property. Our aim is to study properties of Wick multiplication and of Wick versions of holomorphic functions, and to describe a relationship between Wick multiplication and integration, on these spaces. More exactly, we establish that a Wick product of regular test functions is a regular test function; under some conditions a Wick version of a holomorphic function with an argument from the space of regular test functions is a regular test function; show that when employing the Wick multiplication, it is possible to take a time-independent multiplier out of the sign of an extended stochastic integral with respect to a Lévy process; establish an analog of this result for a Pettis integral (a weak integral); obtain a representation of the extended stochastic integral via formal Pettis integral from the Wick product of the original integrand by a Lévy white noise. As an example of an application of our results, we consider an integral stochastic equation with Wick multiplication.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79755437","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
Inverse problem with two unknown time-dependent functions for $2b$-order differential equation with fractional derivative 二阶分数阶微分方程的两个未知时变函数的反问题
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-06-23 DOI: 10.15330/cmp.14.1.213-222
A. Lopushansky, H. Lopushanska
{"title":"Inverse problem with two unknown time-dependent functions for $2b$-order differential equation with fractional derivative","authors":"A. Lopushansky, H. Lopushanska","doi":"10.15330/cmp.14.1.213-222","DOIUrl":"https://doi.org/10.15330/cmp.14.1.213-222","url":null,"abstract":"We study the inverse problem for a differential equation of order $2b$ with a Riemann-Liouville fractional derivative over time and given Schwartz-type distributions in the right-hand sides of the equation and the initial condition. The generalized (time-continuous in a certain sense) solution $u$ of the Cauchy problem for such an equation, the time-dependent continuous young coefficient and a part of a source in the equation are unknown. \u0000In addition, we give the time-continuous values $Phi_j(t)$ of desired generalized solution $u$ of the problem on a fixed test functions $varphi_j(x)$, $xin mathbb R^n$, namely $(u(cdot,t),varphi_j(cdot))=Phi_j(t)$, $tin [0,T]$, $j=1,2$. \u0000We find sufficient conditions for the uniqueness of the generalized solution of the inverse problem throughout the layer $Q:=mathbb R^ntimes [0,T]$ and the existence of a solution in some layer $mathbb R^ntimes [0,T_0]$, $T_0in (0,T]$.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75248019","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
On spectral radius and Nordhaus-Gaddum type inequalities of the generalized distance matrix of graphs 图的广义距离矩阵的谱半径和Nordhaus-Gaddum型不等式
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-06-23 DOI: 10.15330/cmp.14.1.185-193
M. Merajuddin, S. Bhatnagar, S. Pirzada
{"title":"On spectral radius and Nordhaus-Gaddum type inequalities of the generalized distance matrix of graphs","authors":"M. Merajuddin, S. Bhatnagar, S. Pirzada","doi":"10.15330/cmp.14.1.185-193","DOIUrl":"https://doi.org/10.15330/cmp.14.1.185-193","url":null,"abstract":"If $Tr(G)$ and $D(G)$ are respectively the diagonal matrix of vertex transmission degrees and distance matrix of a connected graph $G$, the generalized distance matrix $D_{alpha}(G)$ is defined as $D_{alpha}(G)=alpha ~Tr(G)+(1-alpha)~D(G)$, where $0leq alpha leq 1$. If $rho_1 geq rho_2 geq dots geq rho_n$ are the eigenvalues of $D_{alpha}(G)$, the largest eigenvalue $rho_1$ (or $rho_{alpha}(G)$) is called the spectral radius of the generalized distance matrix $D_{alpha}(G)$. The generalized distance energy is defined as $E^{D_{alpha}}(G)=sum_{i=1}^{n}left|rho_i -frac{2alpha W(G)}{n}right|$, where $W(G)$ is the Wiener index of $G$. In this paper, we obtain the bounds for the spectral radius $rho_{alpha}(G)$ and the generalized distance energy of $G$ involving Wiener index. We derive the Nordhaus-Gaddum type inequalities for the spectral radius and the generalized distance energy of $G$.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76008605","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
Best orthogonal trigonometric approximations of the Nikol'skii-Besov-type classes of periodic functions of one and several variables
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-06-22 DOI: 10.15330/cmp.14.1.171-184
O. Fedunyk-Yaremchuk, S. Hembars’ka
{"title":"Best orthogonal trigonometric approximations of the Nikol'skii-Besov-type classes of periodic functions of one and several variables","authors":"O. Fedunyk-Yaremchuk, S. Hembars’ka","doi":"10.15330/cmp.14.1.171-184","DOIUrl":"https://doi.org/10.15330/cmp.14.1.171-184","url":null,"abstract":"We obtained the exact order estimates of the best orthogonal trigonometric approximations of periodic functions of one and several variables from the Nikol'skii-Besov-type classes $B^{omega}_{1,theta}$ ($B^{Omega}_{1,theta}$ in the multivariate case $dgeq2$) in the space $B_{infty,1}$. We observe that in the multivariate case the orders of mentioned approximation characteristics of the functional classes $B^{Omega}_{1,theta}$ are realized by their approximations by step hyperbolic Fourier sums that contain the necessary number of harmonics. In the univariate case, an optimal in the sense of order estimates for the best orthogonal trigonometric approximations of the corresponding functional classes are the ordinary partial sums of their Fourier series. As a consequence of the obtained results, the exact order estimates of the orthowidths of the classes $B^{omega}_{1,theta}$ ($B^{Omega}_{1,theta}$ for $dgeq2$) in the space $B_{infty,1}$ are also established. Besides, we note that in the univariate case, in contrast to the multivariate one, the estimates of the considered approximation characteristics do not depend on the parameter $theta$.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91106784","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
On statistically convergent complex uncertain sequences 统计收敛的复不确定序列
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-06-17 DOI: 10.15330/cmp.14.1.135-146
B. Das, P. Debnath, B. Tripathy
{"title":"On statistically convergent complex uncertain sequences","authors":"B. Das, P. Debnath, B. Tripathy","doi":"10.15330/cmp.14.1.135-146","DOIUrl":"https://doi.org/10.15330/cmp.14.1.135-146","url":null,"abstract":"In this paper, we extend the study of statistical convergence of complex uncertain sequences in a given uncertainty space. We produce the relation between convergence and statistical convergence in an uncertain environment. We also initiate statistically Cauchy complex uncertain sequence to prove that a complex uncertain sequence is statistically convergent if and only if it is statistically Cauchy. We further characterize a statistically convergent complex uncertain sequence via boundedness and density operator.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83076651","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: 4
Fixed point theorems on an orthogonal metric space using Matkowski type contraction 利用Matkowski型收缩的正交度量空间上的不动点定理
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-06-17 DOI: 10.15330/cmp.14.1.127-134
B. Singh, V. Singh, I. Uddin, Ö. Acar
{"title":"Fixed point theorems on an orthogonal metric space using Matkowski type contraction","authors":"B. Singh, V. Singh, I. Uddin, Ö. Acar","doi":"10.15330/cmp.14.1.127-134","DOIUrl":"https://doi.org/10.15330/cmp.14.1.127-134","url":null,"abstract":"The purpose of this paper is to prove Boyd-Wong and Matkowski type fixed point theorems in orthogonal metric space which was defined by M.E. Gordji in 2017 and is an extension of the metric space. Some examples are established in support of our main results. Finally, we apply our results to establish the existence of a unique solution of a periodic boundary value problem.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81219203","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
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