Abstract In this paper we study the Hadamard product properties of certain class of analytic functions with varying arguments defined by the convolution of Sǎlǎgean and Ruscheweyh derivative. The obtained results are sharp and they improve known results.
{"title":"Modified Hadamard product properties of certain class of analytic functions with varying arguments defined by the convolution of Sǎlǎgean and Ruscheweyh derivative","authors":"Á. O. Páll-Szabó","doi":"10.2478/ausm-2019-0025","DOIUrl":"https://doi.org/10.2478/ausm-2019-0025","url":null,"abstract":"Abstract In this paper we study the Hadamard product properties of certain class of analytic functions with varying arguments defined by the convolution of Sǎlǎgean and Ruscheweyh derivative. The obtained results are sharp and they improve known results.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78096709","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}
Abstract An arbitrary unital ring R is called feebly nil-clean if any its element is of the form q + e − f, where q is a nilpotent and e, f are idempotents with ef = fe. For any commutative ring R and any abelian group G, we find a necessary and sufficient condition when the group ring R(G) is feebly nil-clean only in terms of R, G and their sections. Our result refines establishments due to McGovern et al. in J. Algebra Appl. (2015) on nil-clean rings and Danchev-McGovern in J. Algebra (2015) on weakly nil-clean rings, respectively.
{"title":"Commutative feebly nil-clean group rings","authors":"P. Danchev","doi":"10.2478/ausm-2019-0020","DOIUrl":"https://doi.org/10.2478/ausm-2019-0020","url":null,"abstract":"Abstract An arbitrary unital ring R is called feebly nil-clean if any its element is of the form q + e − f, where q is a nilpotent and e, f are idempotents with ef = fe. For any commutative ring R and any abelian group G, we find a necessary and sufficient condition when the group ring R(G) is feebly nil-clean only in terms of R, G and their sections. Our result refines establishments due to McGovern et al. in J. Algebra Appl. (2015) on nil-clean rings and Danchev-McGovern in J. Algebra (2015) on weakly nil-clean rings, respectively.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75578440","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}
Abstract Barnette’s conjecture states that every three connected cubic bipartite planar graph (CPB3C) is Hamiltonian. In this paper we show the existence of a family of CPB3C Hamiltonian graphs in which large and large subgraphs are non-Hamiltonian.
{"title":"Construction of Barnette graphs whose large subgraphs are non-Hamiltonian","authors":"S. Pirzada, M. Shah","doi":"10.2478/ausm-2019-0026","DOIUrl":"https://doi.org/10.2478/ausm-2019-0026","url":null,"abstract":"Abstract Barnette’s conjecture states that every three connected cubic bipartite planar graph (CPB3C) is Hamiltonian. In this paper we show the existence of a family of CPB3C Hamiltonian graphs in which large and large subgraphs are non-Hamiltonian.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84932785","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}
Abstract We give a new solution to the Rhoades’ open problem on the discontinuity at fixed point via the notion of an S-metric. To do this, we develop a new technique by means of the notion of a Zamfirescu mapping. Also, we consider a recent problem called the “fixed-circle problem” and propose a new solution to this problem as an application of our technique.
{"title":"A new solution to the Rhoades’ open problem with an application","authors":"N. Özgür, N. Taş","doi":"10.2478/ausm-2021-0026","DOIUrl":"https://doi.org/10.2478/ausm-2021-0026","url":null,"abstract":"Abstract We give a new solution to the Rhoades’ open problem on the discontinuity at fixed point via the notion of an S-metric. To do this, we develop a new technique by means of the notion of a Zamfirescu mapping. Also, we consider a recent problem called the “fixed-circle problem” and propose a new solution to this problem as an application of our technique.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81087011","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}
Abstract In this paper, we introduce the use of a powerful tool from theoretical complex analysis, the Blaschke product, for the solution of Riemann-Hilbert problems. Classically, Riemann-Hilbert problems are considered for analytic functions. We give a factorization theorem for meromorphic functions over simply connected nonempty proper open subsets of the complex plane and use this theorem to solve Riemann-Hilbert problems where the given data consists of a meromorphic function.
{"title":"Solving Riemann-Hilbert problems with meromorphic functions","authors":"D. Kučerovský, Aydin Sarraf","doi":"10.2478/ausm-2019-0010","DOIUrl":"https://doi.org/10.2478/ausm-2019-0010","url":null,"abstract":"Abstract In this paper, we introduce the use of a powerful tool from theoretical complex analysis, the Blaschke product, for the solution of Riemann-Hilbert problems. Classically, Riemann-Hilbert problems are considered for analytic functions. We give a factorization theorem for meromorphic functions over simply connected nonempty proper open subsets of the complex plane and use this theorem to solve Riemann-Hilbert problems where the given data consists of a meromorphic function.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77271889","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}
Abstract A subset ℤ ⊆ V(G) of initially colored black vertices of a graph G is known as a zero forcing set if we can alter the color of all vertices in G as black by iteratively applying the subsequent color change condition. At each step, any black colored vertex has exactly one white neighbor, then change the color of this white vertex as black. The zero forcing number ℤ (G), is the minimum number of vertices in a zero forcing set ℤ of G (see [11]). In this paper, we compute the zero forcing number of the degree splitting graph (𝒟𝒮-Graph) and the complete degree splitting graph (𝒞𝒟𝒮-Graph) of a graph. We prove that for any simple graph, ℤ [𝒟𝒮(G)] k + t, where ℤ (G) = k and t is the number of newly introduced vertices in 𝒟𝒮(G) to construct it.
如果可以通过迭代地应用随后的变色条件将图G中所有顶点的颜色都改变为黑色，则图G中初始着色的黑色顶点的一个子集(0≠V(G))称为零强迫集。在每一步中，任何黑色顶点都有一个白色的邻居，然后将这个白色顶点的颜色更改为黑色。零强迫数(G)是零强迫集(G)(见[11])中最小顶点数。本文计算了图的度分裂图(𝒮-Graph)和完全度分裂图(𝒮-Graph)的零强迫数。我们证明了对于任意简单图，n[𝒮(G)] k + t，其中n (G) = k, t是在𝒮(G)中构造它的新引入的顶点的个数。
{"title":"Zero forcing number of degree splitting graphs and complete degree splitting graphs","authors":"C. Dominic","doi":"10.2478/ausm-2019-0004","DOIUrl":"https://doi.org/10.2478/ausm-2019-0004","url":null,"abstract":"Abstract A subset ℤ ⊆ V(G) of initially colored black vertices of a graph G is known as a zero forcing set if we can alter the color of all vertices in G as black by iteratively applying the subsequent color change condition. At each step, any black colored vertex has exactly one white neighbor, then change the color of this white vertex as black. The zero forcing number ℤ (G), is the minimum number of vertices in a zero forcing set ℤ of G (see [11]). In this paper, we compute the zero forcing number of the degree splitting graph (𝒟𝒮-Graph) and the complete degree splitting graph (𝒞𝒟𝒮-Graph) of a graph. We prove that for any simple graph, ℤ [𝒟𝒮(G)] k + t, where ℤ (G) = k and t is the number of newly introduced vertices in 𝒟𝒮(G) to construct it.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77802855","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}
Abstract Let G be a group with identity e and let R be a G-graded ring. In this paper, we introduce and study the concept of gr-n-ideals of R. We obtain many results concerning gr-n-ideals. Some characterizations of gr-n-ideals and their homogeneous components are given.
{"title":"gr-n-ideals in graded commutative rings","authors":"K. Al-Zoubi, Farah Al-Turman, E. Y. Çeli̇kel","doi":"10.2478/ausm-2019-0002","DOIUrl":"https://doi.org/10.2478/ausm-2019-0002","url":null,"abstract":"Abstract Let G be a group with identity e and let R be a G-graded ring. In this paper, we introduce and study the concept of gr-n-ideals of R. We obtain many results concerning gr-n-ideals. Some characterizations of gr-n-ideals and their homogeneous components are given.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76749633","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}
Abstract The aim of this paper is to introduce a new class of hyper-modules that may be called (M, N)-hypermodules over (R, S)-hyperrings. Then, we investigate some properties of this new class of hyperstructures. Since the main tools in the theory of hyperstructures are the fundamental relations, we give some results about them with respect to the fundamental relations.
{"title":"Construction of (M, N)-hypermodule over (R, S)-hyperring","authors":"S. Mirvakili, S. Anvariyeh, B. Davvaz","doi":"10.2478/ausm-2019-0011","DOIUrl":"https://doi.org/10.2478/ausm-2019-0011","url":null,"abstract":"Abstract The aim of this paper is to introduce a new class of hyper-modules that may be called (M, N)-hypermodules over (R, S)-hyperrings. Then, we investigate some properties of this new class of hyperstructures. Since the main tools in the theory of hyperstructures are the fundamental relations, we give some results about them with respect to the fundamental relations.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73467552","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}
Abstract In the present paper we shall introduce some generalized difference Cesàro sequence spaces of fuzzy real numbers defined by Musielak-Orlicz function and -convergence. We make an e ort to study some topological and algebraic properties of these sequence spaces. Furthermore, some inclusion relations between these sequence spaces are establish.
{"title":"On some spaces of Cesàro sequences of fuzzy numbers associated with λ-convergence and Orlicz function","authors":"K. Raj, S. Pandoh","doi":"10.2478/ausm-2019-0013","DOIUrl":"https://doi.org/10.2478/ausm-2019-0013","url":null,"abstract":"Abstract In the present paper we shall introduce some generalized difference Cesàro sequence spaces of fuzzy real numbers defined by Musielak-Orlicz function and -convergence. We make an e ort to study some topological and algebraic properties of these sequence spaces. Furthermore, some inclusion relations between these sequence spaces are establish.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89282711","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}
Abstract In the present paper, we introduce a certain subclass 𝒦q(λ, γ, h) of analytic functions by means of a quasi-subordination. Sharp bounds of the Fekete-Szegő functional for functions belonging to the class 𝒦q(λ, γ, h) are obtained. The results presented in the paper give improved versions for the certain subclasses involving the quasi-subordination and majorization.
{"title":"Sharp bounds of Fekete-Szegő functional for quasi-subordination class","authors":"S. Kant, P. Vyas","doi":"10.2478/ausm-2019-0008","DOIUrl":"https://doi.org/10.2478/ausm-2019-0008","url":null,"abstract":"Abstract In the present paper, we introduce a certain subclass 𝒦q(λ, γ, h) of analytic functions by means of a quasi-subordination. Sharp bounds of the Fekete-Szegő functional for functions belonging to the class 𝒦q(λ, γ, h) are obtained. The results presented in the paper give improved versions for the certain subclasses involving the quasi-subordination and majorization.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72530032","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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