In this paper, we study one dimensional fractional Dirac type systems which includes the right-sided Caputo and the left-sided Riemann-Liouvile fractional derivatives of same order α,α∈(0,1). We investigate the properties of the eigenvalues and the eigenfunctions of this system
{"title":"REGULAR FRACTIONAL DIRAC TYPE SYSTEMS","authors":"B. Allahverdiev, H. Tuna","doi":"10.22190/fumi200318036a","DOIUrl":"https://doi.org/10.22190/fumi200318036a","url":null,"abstract":"In this paper, we study one dimensional fractional Dirac type systems which includes the right-sided Caputo and the left-sided Riemann-Liouvile fractional derivatives of same order α,α∈(0,1). We investigate the properties of the eigenvalues and the eigenfunctions of this system","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87296354","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 second covariant derivative of Riemannian curvature tensor. Some new identities for the second covariant derivative are given. Namely, identities obtained by cyclic sum with respect to three indices are given. In the first case, two curvature tensor indices and one covariant derivative index participate in the cyclic sum, while in the second case one curvature tensor index and two covariant derivative indices participate in the cyclic sum.
{"title":"SOME NEW IDENTITIES FOR THE SECOND COVARIANT DERIVATIVE OF THE CURVATURE TENSOR","authors":"M. Maksimović, M. Stankovic","doi":"10.22190/fumi200930038m","DOIUrl":"https://doi.org/10.22190/fumi200930038m","url":null,"abstract":"In this paper we study the second covariant derivative of Riemannian curvature tensor. Some new identities for the second covariant derivative are given. Namely, identities obtained by cyclic sum with respect to three indices are given. In the first case, two curvature tensor indices and one covariant derivative index participate in the cyclic sum, while in the second case one curvature tensor index and two covariant derivative indices participate in the cyclic sum.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84813023","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 objective of the present research article is to study the $delta$-Lorentzian trans-Sasakian manifolds conceding the $eta$-Ricci solitons and gradient Ricci soliton. We shown that a symmetric second order covariant tensor in a $delta$-Lorentzian trans-Sasakian manifold is a constant multiple of metric tensor. Also, we furnish an example of $eta$-Ricci soliton on 3-diemsional $delta$-Lorentzian trans-Sasakian manifold is provide in the region where $delta$-Lorentzian trans-Sasakian manifold is expanding. Furthermore, we discuss some results based on gradient Ricci solitons on $3$-dimensional $delta$- Lorentzian trans-Sasakian manifold.
{"title":"$eta$-RICCI SOLITONS AND GRADIENT RICCI SOLITONS ON $delta$- LORENTZIAN TRANS-SASAKIAN MANIFOLDS","authors":"M. Siddiqi, M. Akyol","doi":"10.22190/fumi201010039s","DOIUrl":"https://doi.org/10.22190/fumi201010039s","url":null,"abstract":"The objective of the present research article is to study the $delta$-Lorentzian trans-Sasakian manifolds conceding the $eta$-Ricci solitons and gradient Ricci soliton. We shown that a symmetric second order covariant tensor in a $delta$-Lorentzian trans-Sasakian manifold is a constant multiple of metric tensor. Also, we furnish an example of $eta$-Ricci soliton on 3-diemsional $delta$-Lorentzian trans-Sasakian manifold is provide in the region where $delta$-Lorentzian trans-Sasakian manifold is expanding. Furthermore, we discuss some results based on gradient Ricci solitons on $3$-dimensional $delta$- Lorentzian trans-Sasakian manifold.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90753166","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, a new iterative method for solving convex minimization problems over the set of common fixed points of quasi-nonexpansive and demicontractive mappings is constructed. Convergence theorems are also proved in Hilbert spaces without any compactness assumption. As an application, we shall utilize our results to solve quadratic optimization problems involving bounded linear operator. Our theorems are significant improvements on several important recent results.
{"title":"ITERATIVE COMPUTATION FOR SOLVING CONVEX OPTIMIZATION PROBLEMS OVER THE SET OF COMMON FIXED POINTS OF QUASI-NONEXPANSIVE AND DEMICONTRACTIVE MAPPINGS","authors":"T. Sow","doi":"10.22190/fumi190815035s","DOIUrl":"https://doi.org/10.22190/fumi190815035s","url":null,"abstract":"In this paper, a new iterative method for solving convex minimization problems over the set of common fixed points of quasi-nonexpansive and demicontractive mappings is constructed. Convergence theorems are also proved in Hilbert spaces without any compactness assumption. As an application, we shall utilize our results to solve quadratic optimization problems involving bounded linear operator. Our theorems are significant improvements on several important recent results.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72737898","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 will try to study the same result proved in cite{10}. So, on the same model and with some assumptions, we will study the property of homeomorphism of the stochastic flow generated by the natural model in a one-dimensional case and with some modifications, based on an important theory of Hiroshi Kunita. This is the main motivation of our research.
{"title":"THE HOMEOMORPHIC PROPERTY OF THE STOCHASTIC FLOW GENERATED BYTHE ONE-DEFAULT MODEL IN ONE DIMENSIONAL CASE","authors":"Fatima Benziadi","doi":"10.22190/fumi200403037b","DOIUrl":"https://doi.org/10.22190/fumi200403037b","url":null,"abstract":"In this paper, we will try to study the same result proved in cite{10}. So, on the same model and with some assumptions, we will study the property of homeomorphism of the stochastic flow generated by the natural model in a one-dimensional case and with some modifications, based on an important theory of Hiroshi Kunita. This is the main motivation of our research.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72367225","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 has triple main objectives. The first objective is an analysis ofsome auxiliary results on closedness and boundednes of linear relations. The seconde objective is to provide some new characterization results on semiclosed linear relations. Here it is shown that the class of semiclosed linear relations is invariant under finite and countable sums, products, and limits. We obtain some fundamental new results as well as a Kato Rellich Theorem for semiclosed linear relations and essentially interesting generalizations. The last objective concern semiclosed linear relation with closed range, where we have particularly established new characterizations of closable linear relation.
{"title":"NEW RESULTS ON SEMICLOSED LINEAR RELATIONS","authors":"Gherbi Abdellah, Messirdi Bekkai, Messirdi Sanaa","doi":"10.22190/fumi190318034a","DOIUrl":"https://doi.org/10.22190/fumi190318034a","url":null,"abstract":"This paper has triple main objectives. The first objective is an analysis ofsome auxiliary results on closedness and boundednes of linear relations. The seconde objective is to provide some new characterization results on semiclosed linear relations. Here it is shown that the class of semiclosed linear relations is invariant under finite and countable sums, products, and limits. We obtain some fundamental new results as well as a Kato Rellich Theorem for semiclosed linear relations and essentially interesting generalizations. The last objective concern semiclosed linear relation with closed range, where we have particularly established new characterizations of closable linear relation.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82666271","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 deals with different approaches for solving linear systems of the first order differential equations with the system matrix in the symmetric arrowhead form.Some needed algebraic properties of the symmetric arrowhead matrix are proposed.We investigate the form of invariant factors of the arrowhead matrix.Also the entries of the adjugate matrix of the characteristic matrix of the arrowhead matrix are considered. Some reductions techniques for linear systems of differential equations with the system matrix in the arrowhead form are presented.
{"title":"LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS IN ARROWHEAD FORM","authors":"I. Jovović","doi":"10.22190/fumi201115041j","DOIUrl":"https://doi.org/10.22190/fumi201115041j","url":null,"abstract":"This paper deals with different approaches for solving linear systems of the first order differential equations with the system matrix in the symmetric arrowhead form.Some needed algebraic properties of the symmetric arrowhead matrix are proposed.We investigate the form of invariant factors of the arrowhead matrix.Also the entries of the adjugate matrix of the characteristic matrix of the arrowhead matrix are considered. Some reductions techniques for linear systems of differential equations with the system matrix in the arrowhead form are presented.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90259147","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 Weyl type theorems for $f(T)$, where $T$ is algebraically class $p$-$wA(s, t)$ operator with $0 < p leq 1$ and $0 < s, t, s + t leq 1$ and $f$ is an analytic function defined on an open neighborhood of the spectrum of $T$. Also we show that if $A , B^{*} in B(mathcal{H}) $ are class $p$-$wA(s, t)$ operators with $0 < p leq 1$ and $0 < s, t, s + t leq 1$,then generalized Weyl's theorem , a-Weyl's theorem, property $(w)$, property $(gw)$ and generalized a-Weyl's theorem holds for $f(d_{AB})$ for every $f in H(sigma(d_{AB})$, where $ d_{AB}$ denote the generalized derivation $delta_{AB}:B(mathcal{H})rightarrow B(mathcal{H})$ defined by $delta_{AB}(X)=AX-XB$ or the elementary operator $Delta_{AB}:B(mathcal{H})rightarrow B(mathcal{H})$ defined by $Delta_{AB}(X)=AXB-X$.
本文研究了$f(T)$的Weyl型定理，其中$T$是具有$0 < p leq 1$和$0 < s, t, s + t leq 1$的代数类$p$ - $wA(s, t)$算子，$f$是定义在$T$谱的开放邻域上的解析函数。如果$A , B^{*} in B(mathcal{H}) $是$0 < p leq 1$和$0 < s, t, s + t leq 1$类的$p$ - $wA(s, t)$算子，那么对于$f(d_{AB})$，对于每一个$f in H(sigma(d_{AB})$，广义Weyl定理、a-Weyl定理、性质$(w)$、性质$(gw)$和广义a-Weyl定理都成立。其中$ d_{AB}$表示由$delta_{AB}(X)=AX-XB$定义的广义派生$delta_{AB}:B(mathcal{H})rightarrow B(mathcal{H})$或由$Delta_{AB}(X)=AXB-X$定义的初等运算符$Delta_{AB}:B(mathcal{H})rightarrow B(mathcal{H})$。
{"title":"WEYL TYPE THEOREMS FOR ALGEBRIACALLY CLASS $p$-$wA(s,t)$ OPERATORS","authors":"M. Rashid, T. Prasad","doi":"10.22190/fumi201214042r","DOIUrl":"https://doi.org/10.22190/fumi201214042r","url":null,"abstract":"In this paper, we study Weyl type theorems for $f(T)$, where $T$ is algebraically class $p$-$wA(s, t)$ operator with $0 < p leq 1$ and $0 < s, t, s + t leq 1$ and $f$ is an analytic function defined on an open neighborhood of the spectrum of $T$. Also we show that if $A , B^{*} in B(mathcal{H}) $ are class $p$-$wA(s, t)$ operators with $0 < p leq 1$ and $0 < s, t, s + t leq 1$,then generalized Weyl's theorem , a-Weyl's theorem, property $(w)$, property $(gw)$ and generalized a-Weyl's theorem holds for $f(d_{AB})$ for every $f in H(sigma(d_{AB})$, where $ d_{AB}$ denote the generalized derivation $delta_{AB}:B(mathcal{H})rightarrow B(mathcal{H})$ defined by $delta_{AB}(X)=AX-XB$ or the elementary operator $Delta_{AB}:B(mathcal{H})rightarrow B(mathcal{H})$ defined by $Delta_{AB}(X)=AXB-X$.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74389756","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 two systems of generalized Sylvester operator equations. We derive necessary and sufficient conditions for the existence of a solution and provide the general form of a solution. We extend some recent results to more general settings.
{"title":"A NOTE ON SOME SYSTEMS OF GENERALIZED SYLVESTER EQUATIONS","authors":"J. Nikolov Radenković","doi":"10.22190/fumi210210033n","DOIUrl":"https://doi.org/10.22190/fumi210210033n","url":null,"abstract":"In this paper, we study two systems of generalized Sylvester operator equations. We derive necessary and sufficient conditions for the existence of a solution and provide the general form of a solution. We extend some recent results to more general settings.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76179743","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 introduce the concept of I₂-lacunary statistical convergence and strongly I₂-lacunary convergence with respect to the intuitionistic fuzzy norm (μ,v), investigate their relationship, and make some observations about these classes. We mainly examine the relation between these two new methods and the relation between I₂-statistical convergence in the corresponding intuitionistic fuzzy normed space.
{"title":"ON GENERALIZED STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES VIA IDEALS IN INTUITIONISTIC FUZZY NORMED SPACES","authors":"Ö. Kişi","doi":"10.22190/FUMI201027032K","DOIUrl":"https://doi.org/10.22190/FUMI201027032K","url":null,"abstract":"In this paper, we introduce the concept of I₂-lacunary statistical convergence and strongly I₂-lacunary convergence with respect to the intuitionistic fuzzy norm (μ,v), investigate their relationship, and make some observations about these classes. We mainly examine the relation between these two new methods and the relation between I₂-statistical convergence in the corresponding intuitionistic fuzzy normed space.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83867129","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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