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The best approximation of closed operators by bounded operators in Hilbert spaces 希尔伯特空间中有界算子对闭算子的最佳逼近
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-12-30 DOI: 10.15330/cmp.14.2.453-463
V. Babenko, N. Parfinovych, D. Skorokhodov
{"title":"The best approximation of closed operators by bounded operators in Hilbert spaces","authors":"V. Babenko, N. Parfinovych, D. Skorokhodov","doi":"10.15330/cmp.14.2.453-463","DOIUrl":"https://doi.org/10.15330/cmp.14.2.453-463","url":null,"abstract":"We solve the problem of the best approximation of closed operators by linear bounded operators in Hilbert spaces under assumption that the operator transforms orthogonal basis in Hilbert space into an orthogonal system. As a consequence, sharp additive Hardy-Littlewood-Pólya type inequality for multiple closed operators is established. We also demonstrate application of these results in concrete situations: for the best approximation of powers of the Laplace-Beltrami operator on classes of functions defined on closed Riemannian manifolds, for the best approximation of differentiation operators on classes of functions defined on the period and on the real line with the weight $e^{-x^2}$, and for the best approximation of functions of self-adjoint operators in Hilbert spaces.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86725372","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 equitable near-proper coloring of some derived graph classes 若干派生图类的公平近适当着色
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-12-30 DOI: 10.15330/cmp.14.2.529-542
S. Jose, S. Naduvath
{"title":"On equitable near-proper coloring of some derived graph classes","authors":"S. Jose, S. Naduvath","doi":"10.15330/cmp.14.2.529-542","DOIUrl":"https://doi.org/10.15330/cmp.14.2.529-542","url":null,"abstract":"An equitable near-proper coloring of a graph $G$ is a defective coloring in which the number of vertices in any two color classes differ by at most one and the bad edges obtained is minimised by restricting the number of color classes that can have adjacency among their own elements. This paper investigates the equitable near-proper coloring of some derived graph classes like Mycielski graphs, splitting graphs and shadow graphs.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88993296","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
Fekete-Szegö inequality for a subclass of analytic functions associated with Gegenbauer polynomials Fekete-Szegö与Gegenbauer多项式相关的解析函数子类的不等式
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-12-30 DOI: 10.15330/cmp.14.2.582-591
M. Kamali
{"title":"Fekete-Szegö inequality for a subclass of analytic functions associated with Gegenbauer polynomials","authors":"M. Kamali","doi":"10.15330/cmp.14.2.582-591","DOIUrl":"https://doi.org/10.15330/cmp.14.2.582-591","url":null,"abstract":"In this paper, we define a subclass of analytic functions by denote $T_{beta}Hleft( z,C_{n}^{left( lambda right) }left( tright) right) $ satisfying the following subordinate condition begin{equation*} left( 1-beta right) left( frac{zf^{^{prime }}left( zright) }{fleft( zright) }right) +beta left( 1+frac{zf^{^{prime prime }}left( zright) }{f^{^{prime }}left( zright) }right) prec frac{1}{left( 1-2tz+z^{2}right) ^{lambda }}, end{equation*} where $beta geq 0$, $lambda geq 0$ and $tin left( frac{1}{2},1right] $. We give coefficient estimates and Fekete-Szegö inequality for functions belong to this subclass.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85416846","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
Further investigations on unique range set under weight 0 and 1 权值0和1下唯一范围集的进一步研究
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-12-30 DOI: 10.15330/cmp.14.2.504-512
A. Banerjee, S. Maity
{"title":"Further investigations on unique range set under weight 0 and 1","authors":"A. Banerjee, S. Maity","doi":"10.15330/cmp.14.2.504-512","DOIUrl":"https://doi.org/10.15330/cmp.14.2.504-512","url":null,"abstract":"In this paper, we have found the most generalized form of famous Frank-Reinders polynomial. With the help of the same, we have investigated on the unique range set of meromorphic function under two smallest possible weights namely 0 and 1. Our results extend some existing results in the literature.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88495949","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
Weakly symmetric functions on spaces of Lebesgue integrable functions 勒贝格可积函数空间上的弱对称函数
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-12-30 DOI: 10.15330/cmp.14.2.437-441
T. Vasylyshyn, V.A. Zahorodniuk
{"title":"Weakly symmetric functions on spaces of Lebesgue integrable functions","authors":"T. Vasylyshyn, V.A. Zahorodniuk","doi":"10.15330/cmp.14.2.437-441","DOIUrl":"https://doi.org/10.15330/cmp.14.2.437-441","url":null,"abstract":"In this work, we present the notion of a weakly symmetric function. We show that the subset of all weakly symmetric elements of an arbitrary vector space of functions is a vector space itself. Moreover, the subset of all weakly symmetric elements of some algebra of functions is an algebra. Also we consider weakly symmetric functions on the complex Banach space $L_p[0,1]$ of all Lebesgue measurable complex-valued functions on $[0,1]$ for which the $p$th power of the absolute value is Lebesgue integrable. We show that every continuous linear functional on $L_p[0,1],$ where $pin (1,+infty),$ can be approximated by weakly symmetric continuous linear functionals.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88148072","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
Linear Diophantine fuzzy subsets of polygroups 多群的线性丢番图模糊子集
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-12-30 DOI: 10.15330/cmp.14.2.564-581
M. Al Tahan, B. Davvaz, M. Parimala, S. Al-Kaseasbeh
{"title":"Linear Diophantine fuzzy subsets of polygroups","authors":"M. Al Tahan, B. Davvaz, M. Parimala, S. Al-Kaseasbeh","doi":"10.15330/cmp.14.2.564-581","DOIUrl":"https://doi.org/10.15330/cmp.14.2.564-581","url":null,"abstract":"Linear Diophantine fuzzy sets were recently introduced as a generalized form of fuzzy sets. The aim of this paper is to shed the light on the relationship between algebraic hyperstructures and linear Diophantine fuzzy sets through polygroups. More precisely, we introduce the concepts of linear Diophantine fuzzy subpolygroups of a polygroup, linear Diophantine fuzzy normal subpolygroups of a polygroup, and linear Diophantine anti-fuzzy subpolygroups of a polygroup. Furthermore, we study some of their properties and characterize them in relation to level and ceiling sets.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85516802","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 a nonlocal problem for the first-order differential-operator equations 一阶微分算子方程的非局部问题
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-12-30 DOI: 10.15330/cmp.14.2.513-528
V. Horodets’kyi, O. Martynyuk, R. Kolisnyk
{"title":"On a nonlocal problem for the first-order differential-operator equations","authors":"V. Horodets’kyi, O. Martynyuk, R. Kolisnyk","doi":"10.15330/cmp.14.2.513-528","DOIUrl":"https://doi.org/10.15330/cmp.14.2.513-528","url":null,"abstract":"In this work, we study the spaces of generalised elements identified with formal Fourier series and constructed via a non-negative self-adjoint operator in Hilbert space. The spectrum of this operator is purely discrete. For a differential-operator equation of the first order, we formulate a nonlocal multipoint by time problem if the corresponding condition is satisfied in a positive or negative space that is constructed via such operator; such problem can be treated as a generalisation of an abstract Cauchy problem for the specified differential-operator equation. The correct solvability of the aforementioned problem is proven, a fundamental solution is constructed, and its structure and properties are studied. The solution is represented as an abstract convolution of a fundamental solution with a boundary element. This boundary element is used to formulate a multipoint condition, and it is a linear continuous functional defined in the space of main elements. Furthermore, this solution satisfies multipoint condition in a negative space that is adjoint with a corresponding positive space of elements.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87765866","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
Characterization of matrix transformation of complex uncertain sequences via expected value operator 用期望值算子表征复不确定序列的矩阵变换
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-12-02 DOI: 10.15330/cmp.14.2.419-428
B. Das, P. Debnath, B. Tripathy
{"title":"Characterization of matrix transformation of complex uncertain sequences via expected value operator","authors":"B. Das, P. Debnath, B. Tripathy","doi":"10.15330/cmp.14.2.419-428","DOIUrl":"https://doi.org/10.15330/cmp.14.2.419-428","url":null,"abstract":"The aim of this paper is to study the concept of matrix transformation between complex uncertain sequences in mean. The characterization of the matrix transformation has been made by applying the concept of convergence of complex uncertain series. Moreover, in this context, some well-known theorems of real sequence spaces have been established by considering complex uncertain sequence via expected value operator.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78047108","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
Construction of dual-generalized complex Fibonacci and Lucas quaternions 双广义复Fibonacci和Lucas四元数的构造
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-11-21 DOI: 10.15330/cmp.14.2.406-418
G. Y. Şentürk, N. Gürses, S. Yüce
{"title":"Construction of dual-generalized complex Fibonacci and Lucas quaternions","authors":"G. Y. Şentürk, N. Gürses, S. Yüce","doi":"10.15330/cmp.14.2.406-418","DOIUrl":"https://doi.org/10.15330/cmp.14.2.406-418","url":null,"abstract":"The aim of this paper is to construct dual-generalized complex Fibonacci and Lucas quaternions. It examines the properties both as dual-generalized complex number and as quaternion. Additionally, general recurrence relations, Binet's formulas, Tagiuri's (or Vajda's like), Honsberger's, d'Ocagne's, Cassini's and Catalan's identities are obtained. A series of matrix representations of these special quaternions is introduced. Finally, the multiplication of dual-generalized complex Fibonacci and Lucas quaternions are also expressed as their different matrix representations.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76723629","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
Riemann solitons on para-Sasakian geometry 准sasakian几何上的Riemann孤子
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-11-17 DOI: 10.15330/cmp.14.2.395-405
K. De, U. De
{"title":"Riemann solitons on para-Sasakian geometry","authors":"K. De, U. De","doi":"10.15330/cmp.14.2.395-405","DOIUrl":"https://doi.org/10.15330/cmp.14.2.395-405","url":null,"abstract":"The goal of the present article is to investigate almost Riemann soliton and gradient almost Riemann soliton on 3-dimensional para-Sasakian manifolds. At first, it is proved that if $(g, Z,lambda)$ is an almost Riemann soliton on a para-Sasakian manifold $M^3$, then it reduces to a Riemann soliton and $M^3$ is of constant sectional curvature $-1$, provided the soliton vector $Z$ has constant divergence. Besides these, we prove that if $Z$ is pointwise collinear with the characteristic vector field $xi$, then $Z$ is a constant multiple of $xi$ and the manifold is of constant sectional curvature $-1$. Moreover, the almost Riemann soliton is expanding. Furthermore, it is established that if a para-Sasakian manifold $M^3$ admits gradient almost Riemann soliton, then $M^3$ is locally isometric to the hyperbolic space $H^{3}(-1)$. Finally, we construct an example to justify some results of our paper.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91364268","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
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