In this paper, we introduce strong $N_{alpha }^{beta }(theta ,A,F)-$convergence and $S_{alpha }^{beta }(theta ,A,F)-$% convergence with respect to a sequence of modulus functions and give some connections between strongly $N_{alpha }^{beta }(theta ,A,F)-$convergent sequences and $S_{alpha }^{beta }(theta ,A,F)-$convergent sequences for $% 0
{"title":"On $S_{alpha }^{beta }(theta ,A,F)-$convergence and strong $N_{alpha }^{beta }(theta ,A,F)-$convergence","authors":"Hacer Şengül Kandemir, M. Et, H. Cakalli","doi":"10.5269/bspm.51415","DOIUrl":"https://doi.org/10.5269/bspm.51415","url":null,"abstract":"In this paper, we introduce strong $N_{alpha }^{beta }(theta ,A,F)-$convergence and $S_{alpha }^{beta }(theta ,A,F)-$% convergence with respect to a sequence of modulus functions and give some connections between strongly $N_{alpha }^{beta }(theta ,A,F)-$convergent sequences and $S_{alpha }^{beta }(theta ,A,F)-$convergent sequences for $% 0<alpha leq beta leq 1$.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46826020","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}
In this paper we study the structure of arbitrary split regular -Hom-Jordan-Lie super algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular -Hom-Jordan-Lie superalgebra L is of the form L = H [] Σ []2= V []; with H [] a graded linear subspace of the graded abelian subalgebra H and any V [ ]; a well-described ideal of L; satisfying [V [ ]; V []] = 0 if [] ̸= []: Under certain conditions, in the case of L being of maximal length, the simplicity of the algebra is characterized and it is shown that L is the direct sum of the family of its minimal ideals, each one being a simple split regular -Hom-Jordan-Lie superalgebra.
本文研究了任意分裂正则- hom_jordan - lie超代数的结构。通过发展这类代数的根连接技术，我们证明了这样一个分裂正则- hom_jordan - lie超代数L的形式为L = H [] Σ []2= V [];有H[]的有阶阿贝尔子代数H和任意V[]的有阶线性子空间;L的理想;令人满意的[V];V []] = 0, if [] i =[]:在一定条件下，当L是最大长度时，证明了代数的简单性，并证明了L是其最小理想族的直接和，每个理想族都是一个简单的分裂正则- homo - jordan - lie超代数。
{"title":"On the structure of split regular -Hom-Jordan-Lie superalgebras","authors":"Valiollah Khalili","doi":"10.5269/bspm.47798","DOIUrl":"https://doi.org/10.5269/bspm.47798","url":null,"abstract":"In this paper we study the structure of arbitrary split regular -Hom-Jordan-Lie super algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular -Hom-Jordan-Lie superalgebra L is of the form \u0000L = H \u0000[] \u0000 \u0000Σ \u0000[]2= V \u0000[]; with H \u0000[] a graded linear subspace of the graded abelian subalgebra H and any V [ ]; a well-described ideal of L; satisfying [V [ ]; V []] = 0 if [] ̸= []: Under certain conditions, in the case of L being of maximal length, the simplicity of the algebra is characterized and it is shown that L is the direct sum of the family of its minimal ideals, each one being a simple split regular -Hom-Jordan-Lie superalgebra.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45283630","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}
The main purpose of the paper is to bring together two areas in which strong relation, graph theory and topological spaces. And derive interesting formula for the set that contains all minimal dominating sets(MDS) and ( -set). Some separation axioms are discussed in topological graph theory, especially in a cycle graph Cn.
{"title":"Hausdorff of a cycle in topological graph","authors":"A. Jabor, Ahmed Abd-Ali Omran","doi":"10.5269/bspm.52013","DOIUrl":"https://doi.org/10.5269/bspm.52013","url":null,"abstract":"The main purpose of the paper is to bring together two areas in which strong relation, graph theory and topological spaces. And derive interesting formula for the set that contains all minimal dominating sets(MDS) and ( -set). Some separation axioms are discussed in topological graph theory, especially in a cycle graph Cn.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43426897","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}
This paper characterize two bi-linear maps bi-derivations and quasi-multipliers on the module extension Banach algebra $Aoplus_1 X$, where $A$ is a Banach algebra and $X$ is a Banach $A$-module. Under some conditions, it is shown that if every bi-derivation on $Aoplus_1 A$ is inner, then the quotient group of bounded bi-derivations and inner bi-derivations, is equal to space of quasi-multipliers of $A$. Moreover, it is proved that $mathrm{QM}(A oplus_1 A)=mathrm{QM}(A)oplus (mathrm{QM}(A)+mathrm{QM}(A)')$, where $mathrm{QM}(A)'={min mathrm{QM}(A):m(0,a)=m(a,0)=0}$.
{"title":"Bi-derivations and quasi-multipliers on module extensions Banach algebras","authors":"A. Jabbari, A. Ebadian","doi":"10.5269/bspm.52574","DOIUrl":"https://doi.org/10.5269/bspm.52574","url":null,"abstract":"This paper characterize two bi-linear maps bi-derivations and quasi-multipliers on the module extension Banach algebra $Aoplus_1 X$, where $A$ is a Banach algebra and $X$ is a Banach $A$-module. Under some conditions, it is shown that if every bi-derivation on $Aoplus_1 A$ is inner, then the quotient group of bounded bi-derivations and inner bi-derivations, is equal to space of quasi-multipliers of $A$. Moreover, it is proved that $mathrm{QM}(A oplus_1 A)=mathrm{QM}(A)oplus (mathrm{QM}(A)+mathrm{QM}(A)')$, where $mathrm{QM}(A)'={min mathrm{QM}(A):m(0,a)=m(a,0)=0}$.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47109864","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}
The aim of this paper is to introduce a new class of open sets called h-open sets. Also, introduce and study topological properties of hinterior, h-closure, h-limit points, h-derived, h-interior points, h-border, h-frontier and h-exterior by using the concept of h-open sets. Moreover introduce the notion of h-continuous functions, h-open functions, hirresolute functions, h-totally continuous functions, h-contra-continuous functions, h-homeomorphism and investigate some properties of these functions and study some properties, remarks related to them.
{"title":"On h-open sets and h-continuous functions","authors":"F. Abbas","doi":"10.5269/bspm.51006","DOIUrl":"https://doi.org/10.5269/bspm.51006","url":null,"abstract":"The aim of this paper is to introduce a new class of open sets called h-open sets. Also, introduce and study topological properties of hinterior, h-closure, h-limit points, h-derived, h-interior points, h-border, h-frontier and h-exterior by using the concept of h-open sets. Moreover introduce the notion of h-continuous functions, h-open functions, hirresolute functions, h-totally continuous functions, h-contra-continuous functions, h-homeomorphism and investigate some properties of these functions and study some properties, remarks related to them.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41756787","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}
In this article, we introduce a new class of generalized Laguerre-based Frobenius type Eulerian polynomials and then derive diverse explicit and implicit summation formulae and symmetric identities by using series manipulation techniques. Multifarious summation formulas and identities are given earlier for some well known polynomials such as Eulerian polynomials and Frobenius type Eulerian polynomials are generalized.
{"title":"A new class of Laguerre based Frobenius type Eulerian numbers and polynomials","authors":"W. Khan, K. S. Nisar","doi":"10.5269/bspm.52125","DOIUrl":"https://doi.org/10.5269/bspm.52125","url":null,"abstract":"In this article, we introduce a new class of generalized Laguerre-based Frobenius type Eulerian polynomials and then derive diverse explicit and implicit summation formulae and symmetric identities by using series manipulation techniques. Multifarious summation formulas and identities are given earlier for some well known polynomials such as Eulerian polynomials and Frobenius type Eulerian polynomials are generalized.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47609866","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}
In this work, inspired by the technique of the complete transversal, used for the classification of plane branches, developed by Hefez, A. and Hernandes, M., as well as Bruce, J.W., Kirk, N.P. and du Plesis, A.A., study the singularities of applications, we establish a classification of vector fields through their normal forms. In the case of vector fields with non zero linear part in $(mathbb{C}^{2}, 0) $ and nilpotent fields in $(mathbb {C}^{n}, 0), ngeq 2$ we recover the classical normal forms for those fields, and we provide a formal normal form different from Takens in dimension 2. Likewise, we obtain the normal form for the vector fields in $(mathbb{C},0)$ of any multiplicity.
{"title":"Complete transversal and formal normal forms of germs of vector fields","authors":"Soledad Ramírez-Carrasco, Percy Fernández-Sánchez","doi":"10.5269/bspm.46354","DOIUrl":"https://doi.org/10.5269/bspm.46354","url":null,"abstract":"In this work, inspired by the technique of the complete transversal, used for the classification of plane branches, developed by Hefez, A. and Hernandes, M., as well as Bruce, J.W., Kirk, N.P. and du Plesis, A.A., study the singularities of applications, we establish a classification of vector fields through their normal forms. In the case of vector fields with non zero linear part in $(mathbb{C}^{2}, 0) $ and nilpotent fields in $(mathbb {C}^{n}, 0), ngeq 2$ we recover the classical normal forms for those fields, and we provide a formal normal form different from Takens in dimension 2. Likewise, we obtain the normal form for the vector fields in $(mathbb{C},0)$ of any multiplicity.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45098687","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}
In this study, we firstly characterize focal curves by considering quasi frame in the ordinary space. Then, we obtain the relation of each quasi curvatures of curve in terms of focal curvatures. Finally, we give some new conditions with constant quasi curvatures in the ordinary space.
{"title":"On quasi focal curves with quasi frame in space","authors":"T. Körpınar","doi":"10.5269/bspm.50873","DOIUrl":"https://doi.org/10.5269/bspm.50873","url":null,"abstract":"In this study, we firstly characterize focal curves by considering quasi frame in the ordinary space. Then, we obtain the relation of each quasi curvatures of curve in terms of focal curvatures. Finally, we give some new conditions with constant quasi curvatures in the ordinary space.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42621153","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}
The object of this paper is to evaluate some finite double summations relations for the multivariable $A$-function using the summation of a double hypergeometric series. The formulas derived in this paper are most general in character, we also provide a few particular cases for derived summation formulas.
{"title":"Finite summation formulas for the multivariable $A$-function","authors":"D. Kumar, F. Ayant, J. Daiya, K. S. Nisar","doi":"10.5269/bspm.51894","DOIUrl":"https://doi.org/10.5269/bspm.51894","url":null,"abstract":"The object of this paper is to evaluate some finite double summations relations for the multivariable $A$-function using the summation of a double hypergeometric series. The formulas derived in this paper are most general in character, we also provide a few particular cases for derived summation formulas.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42721751","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}
The main purpose of this paper is to introduce a parallel iterative algorithm for approximating the solution of a split feasibility problem on the zero of monotone operators, generalized mixed equilibrium problem and fixed point problem. Using our algorithm, we state and prove a strong convergence theorem for approximating a common element in the set of solutions of a problem of finding zeroes of sum of two monotone operators,generalized mixed equilibrium problem and fixed point problem for a finite family of $eta$-demimetric mappings in the frame work of a reflexive, strictly convex and smooth Banach spaces. We also give a numerical experiment applying our main result. Our result improves, extends and unifies other results in this direction in the literature.
{"title":"Convergence theorem for split feasibility problem, equilibrium problem and zeroes of sum of monotone operators","authors":"O. Oyewole, L. Jolaoso, O. Mewomo, S. H. Khan","doi":"10.5269/bspm.51319","DOIUrl":"https://doi.org/10.5269/bspm.51319","url":null,"abstract":"The main purpose of this paper is to introduce a parallel iterative algorithm for approximating the solution of a split feasibility problem on the zero of monotone operators, generalized mixed equilibrium problem and fixed point problem. Using our algorithm, we state and prove a strong convergence theorem for approximating a common element in the set of solutions of a problem of finding zeroes of sum of two monotone operators,generalized mixed equilibrium problem and fixed point problem for a finite family of $eta$-demimetric mappings in the frame work of a reflexive, strictly convex and smooth Banach spaces. We also give a numerical experiment applying our main result. Our result improves, extends and unifies other results in this direction in the literature.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48785231","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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