Abstract In this paper an improved error bound is obtained for the complete quartic spline with deficiency 2, in the less smooth class of continuous functions. In the case of Lipschitzian functions, the obtained estimate improves the constant from Theorem 3, in J. Approx. Theory 58 (1989) 58-67. Some applications of the complete quartic spline in the numerical integration and in the construction of an iterative numerical method for fourth order two-point boundary value problems with pantograph type delay are presented.
{"title":"Improved error estimate and applications of the complete quartic spline","authors":"A. Bica, D. Curila, Z. Satmari","doi":"10.2478/gm-2019-0016","DOIUrl":"https://doi.org/10.2478/gm-2019-0016","url":null,"abstract":"Abstract In this paper an improved error bound is obtained for the complete quartic spline with deficiency 2, in the less smooth class of continuous functions. In the case of Lipschitzian functions, the obtained estimate improves the constant from Theorem 3, in J. Approx. Theory 58 (1989) 58-67. Some applications of the complete quartic spline in the numerical integration and in the construction of an iterative numerical method for fourth order two-point boundary value problems with pantograph type delay are presented.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"9 1","pages":"71 - 83"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86526719","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 scientific note, an operator, which is the well-known Tremblay operator in the literature, is first introduced and some of its applications to certain analytic complex functions, which are normalized and analytic in the open unit disk, are then determined. In addition, certain special results of the related applications are also emphasized.
{"title":"Certain basic information related to the Tremblay operator and some applications in connection therewith","authors":"H. Irmak","doi":"10.2478/gm-2019-0011","DOIUrl":"https://doi.org/10.2478/gm-2019-0011","url":null,"abstract":"Abstract In this scientific note, an operator, which is the well-known Tremblay operator in the literature, is first introduced and some of its applications to certain analytic complex functions, which are normalized and analytic in the open unit disk, are then determined. In addition, certain special results of the related applications are also emphasized.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"109 1","pages":"13 - 21"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73052685","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 have introduced two new types of sets termed as 𝕀*µ sets and strongly 𝕀*µ -open sets and discussed some of its properties. The relation between similar types of sets, characterizations and some basic properties of such sets have been studied.
{"title":"𝕀*µ open sets in generalized topological spaces","authors":"R. Sen, B. Roy","doi":"10.2478/gm-2019-0013","DOIUrl":"https://doi.org/10.2478/gm-2019-0013","url":null,"abstract":"Abstract In this paper we have introduced two new types of sets termed as 𝕀*µ sets and strongly 𝕀*µ -open sets and discussed some of its properties. The relation between similar types of sets, characterizations and some basic properties of such sets have been studied.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"82 1","pages":"35 - 42"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88171199","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 consider classical entropies associated with several continuous distributions of probabilities. Explicit expressions and properties of them are presented.
摘要:我们考虑与几个连续概率分布相关的经典熵。给出了它们的显式表达式和性质。
{"title":"Entropies related to integral operators","authors":"M. Dancs, A. Mǎdutǎ","doi":"10.2478/gm-2019-0018","DOIUrl":"https://doi.org/10.2478/gm-2019-0018","url":null,"abstract":"Abstract We consider classical entropies associated with several continuous distributions of probabilities. Explicit expressions and properties of them are presented.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"33 1","pages":"107 - 97"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78883730","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 set S ⊆ V is a neighborhood set of a graph G = (V, E), if G = ∪v∈S 〈 N[v] 〉, where 〈 N[v] 〉 is the subgraph of a graph G induced by v and all vertices adjacent to v. A neighborhood set S is said to be a neighbor coloring set if it contains at least one vertex from each color class of a graph G, where color class of a colored graph is the set of vertices having one particular color. The neighbor chromatic number χn (G) is the minimum cardinality of a neighbor coloring set of a graph G. In this article, some results on neighbor chromatic number of Cartesian products of two paths (grid graph) and cycles (torus graphs) are explored.
抽象集合S⊆V是一个社区的一个图G = (V, E),如果G =∪V∈S < N [V] >, < N [V] >是一个图G的子图由V和所有顶点相邻诉邻居集合S是一套邻居着色如果它包含至少一个顶点从每个颜色类图G,在颜色的彩色图是顶点的集合在一个特定的颜色。邻色数χn (G)是图G的邻色集的最小基数。本文讨论了两条路径(网格图)和环面图(环面图)笛卡尔积邻色数的一些结果。
{"title":"On Neighbor chromatic number of grid and torus graphs","authors":"B. Chaluvaraju, C. Appajigowda","doi":"10.2478/gm-2019-0001","DOIUrl":"https://doi.org/10.2478/gm-2019-0001","url":null,"abstract":"Abstract A set S ⊆ V is a neighborhood set of a graph G = (V, E), if G = ∪v∈S 〈 N[v] 〉, where 〈 N[v] 〉 is the subgraph of a graph G induced by v and all vertices adjacent to v. A neighborhood set S is said to be a neighbor coloring set if it contains at least one vertex from each color class of a graph G, where color class of a colored graph is the set of vertices having one particular color. The neighbor chromatic number χn (G) is the minimum cardinality of a neighbor coloring set of a graph G. In this article, some results on neighbor chromatic number of Cartesian products of two paths (grid graph) and cycles (torus graphs) are explored.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"57 1","pages":"15 - 3"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83581229","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 Indulal and Balakrishnan (2016) have put forward the Indu-Bala product and based on this product four new operations are defined by the authors of this manuscript in the paper “Four new operations of graphs based on Indu-Bala product and the Zagreb indices”. In this paper we establish explicit formulas of the forgotten topological index and reduced second Zagreb index in connection with these new operations of graphs.
{"title":"Forgotten topological index and reduced Zagreb index of four new operations of graphs","authors":"A. Bharali, A. Mahanta, J. Buragohain","doi":"10.2478/gm-2019-0005","DOIUrl":"https://doi.org/10.2478/gm-2019-0005","url":null,"abstract":"Abstract Indulal and Balakrishnan (2016) have put forward the Indu-Bala product and based on this product four new operations are defined by the authors of this manuscript in the paper “Four new operations of graphs based on Indu-Bala product and the Zagreb indices”. In this paper we establish explicit formulas of the forgotten topological index and reduced second Zagreb index in connection with these new operations of graphs.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"33 1","pages":"45 - 56"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87106968","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 find accordance of some classical inequalities and fractional dynamic inequalities. We find inequalities such as Radon’s inequality, Bergström’s inequality, Rogers-Hölder’s inequality, Cauchy-Schwarz’s inequality, the weighted power mean inequality and Schlömilch’s inequality in generalized and extended form by using the Riemann-Liouville fractional integrals on time scales.
{"title":"Consensus of classical and fractional inequalities having congruity on time scale calculus","authors":"Muhammad Jibril Shahab Sahir","doi":"10.2478/gm-2019-0006","DOIUrl":"https://doi.org/10.2478/gm-2019-0006","url":null,"abstract":"Abstract In this paper, we find accordance of some classical inequalities and fractional dynamic inequalities. We find inequalities such as Radon’s inequality, Bergström’s inequality, Rogers-Hölder’s inequality, Cauchy-Schwarz’s inequality, the weighted power mean inequality and Schlömilch’s inequality in generalized and extended form by using the Riemann-Liouville fractional integrals on time scales.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"20 1","pages":"57 - 69"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91306558","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 investigate the existence of solution of integro-differential equations (IDEs) with Hilfer-Hadamard fractional derivative. The main results are obtained by using Schaefer’s fixed point theorem. Some Ulam stability results are presented.
{"title":"A study of fractional integro-differential equations via Hilfer-Hadamard fractional derivative","authors":"D. Vivek, K. Kanagarajan, E. Elsayed","doi":"10.2478/gm-2019-0007","DOIUrl":"https://doi.org/10.2478/gm-2019-0007","url":null,"abstract":"Abstract In this paper, we investigate the existence of solution of integro-differential equations (IDEs) with Hilfer-Hadamard fractional derivative. The main results are obtained by using Schaefer’s fixed point theorem. Some Ulam stability results are presented.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"3 1","pages":"71 - 84"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83688521","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 This paper mainly dedicated on overview of zero sets in Ideal topological spaces. We also introduce a new class of functions which generalizes the class of continuous functions and investigate its position in the hierarchy of continuous functions on Ideal topological spaces. Moreover, these new sets (zero*-ℐ-set) which is a pragmatic approach to characterize completely Hausdorff spaces.
摘要本文主要对理想拓扑空间中的零集进行了综述。我们还引入了一类新的函数，它是连续函数类的推广，并研究了它在理想拓扑空间上连续函数层次中的位置。此外，这些新的集合(0 *- k -集)是表征完全Hausdorff空间的一种实用方法。
{"title":"Some strong and weak form of z-continuity via Cl*","authors":"A. Prasannan, J. Biswas","doi":"10.2478/gm-2019-0008","DOIUrl":"https://doi.org/10.2478/gm-2019-0008","url":null,"abstract":"Abstract This paper mainly dedicated on overview of zero sets in Ideal topological spaces. We also introduce a new class of functions which generalizes the class of continuous functions and investigate its position in the hierarchy of continuous functions on Ideal topological spaces. Moreover, these new sets (zero*-ℐ-set) which is a pragmatic approach to characterize completely Hausdorff spaces.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"42 1","pages":"101 - 85"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81413585","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 consider two continuous functions f, g : [a, b] → ℝ and we study for these ones, under which circumstances the intermediate point function is four order di erentiable at the point x = a and we calculate its derivative.
{"title":"Properties of the intermediate point from a mean value theorem of the integral calculus - II","authors":"Emilia-Loredana Pop, D. Duca, A. Raţiu","doi":"10.2478/gm-2019-0003","DOIUrl":"https://doi.org/10.2478/gm-2019-0003","url":null,"abstract":"Abstract In this paper we consider two continuous functions f, g : [a, b] → ℝ and we study for these ones, under which circumstances the intermediate point function is four order di erentiable at the point x = a and we calculate its derivative.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"13 1","pages":"29 - 36"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75647808","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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