Pub Date : 2022-12-30DOI: 10.15330/cmp.14.2.442-452
O. H. Edely, M. Mursaleen
In [Analysis 1985, 5 (4), 301-313], J.A. Fridy proved an equivalence relation between statistical convergence and statistical Cauchy sequence. In this paper, we define $A^{I^{ast }}$-statistical convergence and find under certain conditions, that it is equivalent to $A^{I}$-statistical convergence defined in [Appl. Math. Lett. 2012, 25 (4), 733-738]. Moreover, we define $A^{I}$- and $A^{I^{ast }}$-statistical Cauchy sequences and find some equivalent relation with $A^{I}$- and $A^{I^{ast }}$-statistical convergence.
J.A. Fridy在[Analysis 1985,5(4)， 301-313]中证明了统计收敛与统计柯西序列之间的等价关系。本文定义了$A^{I^{ast}}$-统计收敛性，并发现在一定条件下，它等价于[Appl]中定义的$A^{I}$-统计收敛性。数学。生态学报，2012,25(4)，733-738。此外，我们定义了$A^{I}$-和$A^{I^{ast}}$-统计柯西序列，并找到了$A^{I}$-和$A^{I^{ast}}$-统计收敛的等价关系。
{"title":"On $A$-statistical convergence and $A$-statistical Cauchy via idea","authors":"O. H. Edely, M. Mursaleen","doi":"10.15330/cmp.14.2.442-452","DOIUrl":"https://doi.org/10.15330/cmp.14.2.442-452","url":null,"abstract":"In [Analysis 1985, 5 (4), 301-313], J.A. Fridy proved an equivalence relation between statistical convergence and statistical Cauchy sequence. In this paper, we define $A^{I^{ast }}$-statistical convergence and find under certain conditions, that it is equivalent to $A^{I}$-statistical convergence defined in [Appl. Math. Lett. 2012, 25 (4), 733-738]. Moreover, we define $A^{I}$- and $A^{I^{ast }}$-statistical Cauchy sequences and find some equivalent relation with $A^{I}$- and $A^{I^{ast }}$-statistical convergence.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"50 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73314077","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}
Pub Date : 2022-12-30DOI: 10.15330/cmp.14.2.582-591
M. Kamali
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.
{"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":"175 1","pages":""},"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}
Pub Date : 2022-12-30DOI: 10.15330/cmp.14.2.529-542
S. Jose, S. Naduvath
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.
{"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":"28 1","pages":""},"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}
Pub Date : 2022-12-30DOI: 10.15330/cmp.14.2.504-512
A. Banerjee, S. Maity
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.
{"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":"5 1","pages":""},"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}
Pub Date : 2022-12-30DOI: 10.15330/cmp.14.2.564-581
M. Al Tahan, B. Davvaz, M. Parimala, S. Al-Kaseasbeh
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.
{"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":"28 1","pages":""},"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}
Pub Date : 2022-12-30DOI: 10.15330/cmp.14.2.437-441
T. Vasylyshyn, V.A. Zahorodniuk
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.
{"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":"7 1","pages":""},"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}
Pub Date : 2022-12-30DOI: 10.15330/cmp.14.2.513-528
V. Horodets’kyi, O. Martynyuk, R. Kolisnyk
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.
{"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":"29 1","pages":""},"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}
Pub Date : 2022-12-02DOI: 10.15330/cmp.14.2.419-428
B. Das, P. Debnath, B. Tripathy
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.
{"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":"36 1","pages":""},"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}
Pub Date : 2022-11-21DOI: 10.15330/cmp.14.2.406-418
G. Y. Şentürk, N. Gürses, S. Yüce
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.
{"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":"37 1","pages":""},"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}
Pub Date : 2022-11-17DOI: 10.15330/cmp.14.2.395-405
K. De, U. De
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.
{"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":"1 1","pages":""},"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}
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