{"title":"Lacunary statistically convergence via modulus function sequences","authors":"Erdal Bayram, Çiğdem Bektaş","doi":"10.36753/mathenot.1477450","DOIUrl":"https://doi.org/10.36753/mathenot.1477450","url":null,"abstract":"Modifying the definition of density functions is one method used to generalise statistical convergence. In the present study, we use sequences of modulus functions and order $alpha in left( 0,1right] $ to introduce a new density. Based on this density framework, we define strong $(f_k)$-lacunary summability of order $alpha $ and $(f_k)$-lacunary statistical convergence of order $alpha $ for a sequence of modulus functions $(f_k)$. This concept holds an intermediate position between the usual convergence and the statistical convergence for lacunary sequences. We also establish inclusion theorems and relations between these two concepts in the study.","PeriodicalId":489457,"journal":{"name":"Mathematical sciences and applications e-notes","volume":"6 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141796785","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}
{"title":"On the $q$-Ces`{a}ro bounded double sequence space","authors":"Sezer Erdem","doi":"10.36753/mathenot.1492238","DOIUrl":"https://doi.org/10.36753/mathenot.1492238","url":null,"abstract":"In this article, the new sequence space $tilde{mathcal{M}}_u^q$ is acquainted, described as the domain of the 4d (4-dimensional) $q$-Ces`{a}ro matrix operator, which is the $q$-analogue of the first order 4d Ces`{a}ro matrix operator, on the space of bounded sequences. In the continuation of the study, the completeness of the new space is given, its fundamental set is found, and the inclusion relation related to the space is presented. In the last two parts, the duals of the space are determined and some matrix classes are acquired.","PeriodicalId":489457,"journal":{"name":"Mathematical sciences and applications e-notes","volume":"1 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141662922","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}
{"title":"TAYLOR’S POWER LAW AND PACKING CIRCLES","authors":"Oğuzhan Kaya, Zeki Topçu","doi":"10.36753/mathenot.1448644","DOIUrl":"https://doi.org/10.36753/mathenot.1448644","url":null,"abstract":"We show that the circle packing problem in $mathbb R^2$ satisfies the Taylor power law formula for $b=2$.","PeriodicalId":489457,"journal":{"name":"Mathematical sciences and applications e-notes","volume":"29 41","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141684495","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}
A. Ademola, A. Aderogba, Opeoluwa Lawrence Ogundipe, Gbenga Akinbo, B. Onasanya
{"title":"Asymptotic Stability of Neutral Differential Systems with Variable Delay and Nonlinear Perturbations","authors":"A. Ademola, A. Aderogba, Opeoluwa Lawrence Ogundipe, Gbenga Akinbo, B. Onasanya","doi":"10.36753/mathenot.1320286","DOIUrl":"https://doi.org/10.36753/mathenot.1320286","url":null,"abstract":"In this paper, the problem of asymptotic stability of a kind of nonlinear perturbed neutral differential system with variable delay is discussed. The Lyapunov-Krasovskiv{i} functional constructed, is used to obtain conditions for asymptotic stability of the nonlinear perturbed neutral differential system in terms of linear matrix inequality (LMI). The two new results (delay-independent and delay-dependent criteria) include and extend the existing results in the literature. Finally, an example of delay-dependent criteria is supplied and the simulation result is shown to justify the effectiveness and reliability of the used techniques.","PeriodicalId":489457,"journal":{"name":"Mathematical sciences and applications e-notes","volume":"88 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139601815","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}
{"title":"Some New f-Divergence Measures and Their Basic Properties","authors":"Sever Dragomir","doi":"10.36753/mathenot.1362706","DOIUrl":"https://doi.org/10.36753/mathenot.1362706","url":null,"abstract":"In this paper we introduce some new f-divergence measures that we call t-asymmetric/symmetric divergence measure and integral divergence measure, establish their joint convexity and provide some inequalities that connect these f-divergences to the classical one intyroduced by Csiszar in 1963. Applications for the dichotomy class of convex functions are provided as well.","PeriodicalId":489457,"journal":{"name":"Mathematical sciences and applications e-notes","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139536261","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}
{"title":"The Source of $Gamma$-primeness on $Gamma$-rings","authors":"Didem Yeşil, Rasie Mekera","doi":"10.36753/mathenot.1389757","DOIUrl":"https://doi.org/10.36753/mathenot.1389757","url":null,"abstract":"The source of the primeness texture is a skeleton that generalizes traditional prime rings. In this context, our primary aim in this study is to describe the source of $Gamma$-primeness in $Gamma$-rings not included in the literature. \u0000 This work's purpose is to generalize the concept of the source of primeness to a $Gamma$-ring. In this study, the characteristics provided by the defined concept are also discussed, and the results achieved are exemplified.","PeriodicalId":489457,"journal":{"name":"Mathematical sciences and applications e-notes","volume":"29 48","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139630859","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}
{"title":"The Farey sum of Pythagorean and Eisenstein triples","authors":"M. Crasmareanu","doi":"10.36753/mathenot.1316554","DOIUrl":"https://doi.org/10.36753/mathenot.1316554","url":null,"abstract":"A composition law, inspired by the Farey addition, is introduced on the set of Pythagorean triples. We study some of its properties as well as two symmetric matrices naturally associated to a given Pythagorean triple. Several examples are discussed, some of them involving the degenerated Pythagorean triple $(1, 0, 1)$. The case of Eisenstein triples is also presented.","PeriodicalId":489457,"journal":{"name":"Mathematical sciences and applications e-notes","volume":"95 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138599794","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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