c{S}ahsene Alti nkaya, Yeliz Kara, Yeşim Sağlam Özkan
This research paper deals with some radius problems, the basic geometricproperties, general coecient and inclusion relations that are established for functionsin a general subfamily of analytic functions subordinate to k-Jacobsthal numbers.
{"title":"BASIC APPLICATIONS OF THE q-DERIVATIVE FOR A GENERAL SUBFAMILY OF ANALYTIC FUNCTIONS SUBORDINATE TO k-JACOBSTHAL NUMBERS","authors":"c{S}ahsene Alti nkaya, Yeliz Kara, Yeşim Sağlam Özkan","doi":"10.22190/fumi211201022a","DOIUrl":"https://doi.org/10.22190/fumi211201022a","url":null,"abstract":"This research paper deals with some radius problems, the basic geometricproperties, general coecient and inclusion relations that are established for functionsin a general subfamily of analytic functions subordinate to k-Jacobsthal numbers.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"338 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80694867","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}
We give some characterizations for submanifolds admitting almost $eta$-Ricci-Bourguignon solitons whose potential vector field is the tangential component of a concurrent vector field on the ambient manifold. We describe the particular cases of umbilical submanifolds and of hypersurfaces in a space with constant curvature.
{"title":"REMARKS ON SUBMANIFOLDS AS ALMOST eta-RICCI-BOURGUIGNON SOLITONS","authors":"A. Blaga, Cihan Ozgur","doi":"10.22190/fumi220318027b","DOIUrl":"https://doi.org/10.22190/fumi220318027b","url":null,"abstract":"We give some characterizations for submanifolds admitting almost $eta$-Ricci-Bourguignon solitons whose potential vector field is the tangential component of a concurrent vector field on the ambient manifold. We describe the particular cases of umbilical submanifolds and of hypersurfaces in a space with constant curvature.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75458087","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 class of cubic (alpha, beta)-metrics. We show that every weakly Landsberg cubic (alpha, beta)-metric has vanishing S-curvature. Using it, we prove that cubic (alpha, beta)-metric is a weakly Landsberg metric if and only if it is a Berwald metric. This yields an extension of the Matsumoto's result for Landsberg cubic metric.
{"title":"ON CUBIC (alpha, beta)-METRICS IN FINSLER GEOMETRY","authors":"Hosein Tondro Vishkaei, A. Tayebi","doi":"10.22190/fumi220323030t","DOIUrl":"https://doi.org/10.22190/fumi220323030t","url":null,"abstract":"In this paper, we study the class of cubic (alpha, beta)-metrics. We show that every weakly Landsberg cubic (alpha, beta)-metric has vanishing S-curvature. Using it, we prove that cubic (alpha, beta)-metric is a weakly Landsberg metric if and only if it is a Berwald metric. This yields an extension of the Matsumoto's result for Landsberg cubic metric.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85158621","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}
Integral representations for a generalized Mathieu series and its companions are used to undertake analysis leading to novel insights for Zeta and Dirichlet Beta function families. The bounds are procured using sharp bounds of Zeta and Dirichlet family bounds to procure approximating and bounds utilising integral representation of generalized Mathieu series results using in particular Hardy-type upper bounds.
{"title":"ON ZETA AND DIRICHLET BETA FUNCTION FAMILIES AS GENERATORS OF GENERALIZED MATHIEU SERIES, PROVIDING APPROXIMATION AND BOUNDS","authors":"P. Cerone","doi":"10.22190/fumi210519018c","DOIUrl":"https://doi.org/10.22190/fumi210519018c","url":null,"abstract":"Integral representations for a generalized Mathieu series and its companions are used to undertake analysis leading to novel insights for Zeta and Dirichlet Beta function families. The bounds are procured using sharp bounds of Zeta and Dirichlet family bounds to procure approximating and bounds utilising integral representation of generalized Mathieu series results using in particular Hardy-type upper bounds.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"183 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74652729","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 analyze various classes of multi-dimensional Stepanov $rho$-almost periodic functions in general metric. The main structural properties for the introduced classes of Stepanov almost periodic type functions are established. We also provide an illustrative application to the abstract degenerate semilinear fractional differential equations.
{"title":"STEPANOV $rho$-ALMOST PERIODIC FUNCTIONS IN GENERAL METRIC","authors":"M. Kostic","doi":"10.22190/fumi211217024k","DOIUrl":"https://doi.org/10.22190/fumi211217024k","url":null,"abstract":"In this paper, we analyze various classes of multi-dimensional Stepanov $rho$-almost periodic functions in general metric. The main structural properties for the introduced classes of Stepanov almost periodic type functions are established. We also provide an illustrative application to the abstract degenerate semilinear fractional differential equations.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"25 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82597142","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 the present paper is to give some characterizations of α-cosymplectic manifolds admitting ∗-conformal Ricci solitons. Such manifolds with gradient ∗-conformal Ricci solitons have also been considered
{"title":"SOME CHARACTERIZATIONS OF α-COSYMPLECTIC MANIFOLDS ADMITTING ∗-CONFORMAL RICCI SOLITIONS","authors":"Sudipto Kumar Das, A. Sarkar","doi":"10.22190/fumi220320028d","DOIUrl":"https://doi.org/10.22190/fumi220320028d","url":null,"abstract":"The object of the present paper is to give some characterizations of α-cosymplectic manifolds admitting ∗-conformal Ricci solitons. Such manifolds with gradient ∗-conformal Ricci solitons have also been considered","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"64 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85007680","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}
We prove that if an $eta$-Einstein para-Kenmotsu manifold admits a $eta$-Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a $eta$-Ricci soliton is Einstein if its potential vector field $V$ is infinitesimal paracontact transformation or collinear with the Reeb vector field. Further, we prove that if a para-Kenmotsu manifold admits a gradient almost $eta$-Ricci soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits $eta$-Ricci soliton and satisfy our results. We also have studied $eta$-Ricci soliton in 3-dimensional normal almost paracontact metric manifolds and we show that if in a 3-dimensional normal almost paracontact metric manifold with $alpha, beta $ = constant, the metric is $eta$-Ricci soliton, where potential vector field $V$ is collinear with the characteristic vector field $xi$, then the manifold is $eta$-Einstein manifold.
{"title":"CERTAIN RESULTS ON $eta$-RICCI SOLITIONS AND ALMOST $eta$-RICCI SOLITONS","authors":"S. Dey, S. Azami","doi":"10.22190/fumi220210025d","DOIUrl":"https://doi.org/10.22190/fumi220210025d","url":null,"abstract":"We prove that if an $eta$-Einstein para-Kenmotsu manifold admits a $eta$-Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a $eta$-Ricci soliton is Einstein if its potential vector field $V$ is infinitesimal paracontact transformation or collinear with the Reeb vector field. Further, we prove that if a para-Kenmotsu manifold admits a gradient almost $eta$-Ricci soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits $eta$-Ricci soliton and satisfy our results. We also have studied $eta$-Ricci soliton in 3-dimensional normal almost paracontact metric manifolds and we show that if in a 3-dimensional normal almost paracontact metric manifold with $alpha, beta $ = constant, the metric is $eta$-Ricci soliton, where potential vector field $V$ is collinear with the characteristic vector field $xi$, then the manifold is $eta$-Einstein manifold.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"25 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85182055","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 warped product manifolds admitting $tau$-quasi Ricci-harmonic(RH) metrics. We prove that the metric of the fibre is harmonic Einstein when warped product metric is $tau$-quasi RH metric. We also provide some conditions for $M$ to be a harmonic Einstein manifold. Finally, we provide necessary and sufficient conditions for a metric $g$ to be $tau$-quasi RH metric by using a differential equation system.
{"title":"ON WARPED PRODUCT MANIFOLDS ADMITTING τ-QUASI RICCI-HARMONIC METRICS","authors":"S. Günsen, L. Onat","doi":"10.22190/fumi211212023g","DOIUrl":"https://doi.org/10.22190/fumi211212023g","url":null,"abstract":"In this paper, we study warped product manifolds admitting $tau$-quasi Ricci-harmonic(RH) metrics. We prove that the metric of the fibre is harmonic Einstein when warped product metric is $tau$-quasi RH metric. We also provide some conditions for $M$ to be a harmonic Einstein manifold. Finally, we provide necessary and sufficient conditions for a metric $g$ to be $tau$-quasi RH metric by using a differential equation system.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"49 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87133821","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, fractional differential equations in the sense of Caputo-Fabrizio derivative are transformed into integral equations. Then a high order numerical method for the integral equation is investigated by approximating the integrand with a piece-wise quadratic interpolant. The scheme is capable of handling both linear and nonlinear fractional differential equations. A detailed error analysis and stability region of the numerical scheme is rigorously established.
{"title":"A NEW NUMERICAL METHOD FOR SOLVING FRACTIONAL NEW NUMERICAL METHOD FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS IN THE SENSE OF CAPUTO-FABRIZIO DERIVATIVE","authors":"Leila Moghadam Dizaj Herik, M. Javidi, M. Shafiee","doi":"10.22190/fumi210105006m","DOIUrl":"https://doi.org/10.22190/fumi210105006m","url":null,"abstract":"In this paper, fractional differential equations in the sense of Caputo-Fabrizio derivative are transformed into integral equations. Then a high order numerical method for the integral equation is investigated by approximating the integrand with a piece-wise quadratic interpolant. The scheme is capable of handling both linear and nonlinear fractional differential equations. A detailed error analysis and stability region of the numerical scheme is rigorously established.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"114 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78935205","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 number of the cycles in a graph is an important well-known parameter in graph theory and there are a lot of investigations carried out in the literature for finding suitable bounds for it. In this paper, we delve into studying this parameter and the cycle structure of graphs through the lens of the cycle hypergraphs and VC-dimension and find some new bounds for it, where the cycle hypergraph of a graph is a hypergraph with the edges of the graph as its vertices and the edge sets of the cycles as its hyperedges respectively. Note that VC-dimension is an important notion in extremal combinatorics, graph theory, statistics and machine learning. We investigate cycle hypergraph from the perspective of VC-theory, specially the celebrated Sauer-Shelah lemma, in order to give our upper and lower bounds for the number of the cycles in terms of the (dual) VC-dimension of the cycle hypergraph and nullity of graph. We compute VC-dimension and the mentioned bounds in some graph classes and also show that in certain classes, our bounds are sharper than many previous ones in the literature.
{"title":"ON THE NUMBER OF CYCLES OF GRAPHS AND VC-DIMENSION","authors":"A. Mofidi","doi":"10.22190/fumi210301011m","DOIUrl":"https://doi.org/10.22190/fumi210301011m","url":null,"abstract":"The number of the cycles in a graph is an important well-known parameter in graph theory and there are a lot of investigations carried out in the literature for finding suitable bounds for it. In this paper, we delve into studying this parameter and the cycle structure of graphs through the lens of the cycle hypergraphs and VC-dimension and find some new bounds for it, where the cycle hypergraph of a graph is a hypergraph with the edges of the graph as its vertices and the edge sets of the cycles as its hyperedges respectively. Note that VC-dimension is an important notion in extremal combinatorics, graph theory, statistics and machine learning. We investigate cycle hypergraph from the perspective of VC-theory, specially the celebrated Sauer-Shelah lemma, in order to give our upper and lower bounds for the number of the cycles in terms of the (dual) VC-dimension of the cycle hypergraph and nullity of graph. We compute VC-dimension and the mentioned bounds in some graph classes and also show that in certain classes, our bounds are sharper than many previous ones in the literature.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"46 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76613751","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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