{"title":"Generalized convergence and generalized sequential spaces","authors":"V. Renukadevi, P. Vijayashanthi","doi":"10.37193/cmi.2022.02.06","DOIUrl":"https://doi.org/10.37193/cmi.2022.02.06","url":null,"abstract":"We continue the study of g-convergence given in 2005 [Caldas, M.; Jafari, S. On $g$-US spaces. {em Stud. Cercet. c{S}tiinc{t}. Ser. Mat. Univ. Bacu{a}u} {bf 14} (2004), 13--19 (2005).] by introducing the sequential $g$-closure operator and we prove that the product of $g$-sequential spaces is not $g$-sequential by giving an example. We further investigate sequential $g$-continuity in topological spaces and present interesting theorems which are also new for the real case. It is shown that in a topological space the property of being $g$-sequential implies sequential, $g$-Fr'echet implies Fr'echet and $g$-Fr'echet implies $g$-sequential. However, the inverse conclusions are not true and some counter examples are given. Also, we show that strongly $g$-continuous image of a $g$-sequential space is $g$-sequential, if the map is quotient. Finally, we obtain a necessary and sufficient condition for a topological space to be $g$-sequential in terms of a sequentially $g$-quotient map.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133283234","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 results on star-line graphs","authors":"S. Varghese","doi":"10.37193/cmi.2022.02.12","DOIUrl":"https://doi.org/10.37193/cmi.2022.02.12","url":null,"abstract":"\"Let $H$ be a connected graph with at least three vertices. The $H$-line graph, $HL(G)$, of a graph $G$ has all the edges of $G$ as its vertices, two vertices of $HL(G)$ are adjacent if the corresponding edges in $G$ are adjacent and belong to a common copy of $H$. In this paper we investigate some properties of the star-line graph $K_{1,n}L(G)$ of a graph $G$. We also obtain a Krausz type characterization for star-line graphs. Traversability of star-line graphs is also studied.\"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122231120","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":"Fold thickness of some classes of graphs","authors":"Reji Thankachan, Vaishnavi Sidharthan","doi":"10.37193/cmi.2022.02.11","DOIUrl":"https://doi.org/10.37193/cmi.2022.02.11","url":null,"abstract":"A 1-fold of $G$ is the graph $G'$ obtained from a graph $G$ by identifying two nonadjacent vertices in $G$ having at least one common neighbor and reducing the resulting multiple edges to simple edges. A sequence of graphs $G = G_0, G_1, G_2, ldots ,G_k$, where $G_{i+1}$ is a 1-fold of $G_{i}$ for $i=0,1,2,ldots ,k-1$ is called a uniform $k$-folding if all the graphs in the sequence are singular or all of them are nonsingular. The largest $k$ for which there exists a uniform $k$- folding of $G$ is called fold thickness of $G$ and it was first introduced in [Campe{~n}a, F. J. H.; Gervacio, S. V. On the fold thickness of graphs. emph{Arab, J. Math. (Springer)} {bf9} (2020), no. 2, 345--355]. In this paper, we determine fold thickness of $K_n odot overline{K_m}$, $K_n + overline{K_m}$, cone graph and tadpole graph.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128574445","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":"Fuzzy Minimal and Maximal δ-Open Sets","authors":"S. Joseph, D. Kirubaharan","doi":"10.37193/cmi.2022.02.05","DOIUrl":"https://doi.org/10.37193/cmi.2022.02.05","url":null,"abstract":"The aim of this article is to introduce fuzzy minimal $delta$-open and fuzzy maximal $delta$-open sets in fuzzy topological space. Further, we investigate some properties with these new sets.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117251744","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":"\"D-Fuzzy set and its applications in decision making problems\"","authors":"J. Srivastava, Sudhir Maddheshiya","doi":"10.37193/cmi.2022.01.12","DOIUrl":"https://doi.org/10.37193/cmi.2022.01.12","url":null,"abstract":"\"In this paper we have presented an approach to deal with decision making problems. For this purpose we have constructed a fuzzy set, namely D-fuzzy set, for a soft set. This concept of D-fuzzy set will also be used when the information is given in form of weighted soft set, fuzzy soft set or weighted fuzzy soft set. Further we will apply this method when there are more than one observer. We will define such sets as multi-observer soft set, multi-observer weighted soft set etc.\"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133479158","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":"\"Why Pompeiu-Hausdorff metric instead of Hausdorff metric?\"","authors":"V. Berinde, M. Pacurar","doi":"10.37193/cmi.2022.01.03","DOIUrl":"https://doi.org/10.37193/cmi.2022.01.03","url":null,"abstract":"\"The distance between two sets, commonly called Hausdorff metric, is a very important mathematical concept, with plenty of applications in almost all scientific research areas. We suggest in this paper an update of its name as Pompeiu-Hausdorff metric (distance). Based on historical evidence, this proposal follows the contemporary manner of appointing concepts in scientific writings, especially in mathematics.\"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"140 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114730315","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 inequalities on the Mostar index","authors":"Özge Çolakoǧlu Havare","doi":"10.37193/cmi.2022.01.07","DOIUrl":"https://doi.org/10.37193/cmi.2022.01.07","url":null,"abstract":"\"Topological indices are the numerical descriptors of a molecular structure obtained via molecular graph G. They are used to predict physicochemical and bioactive properties of the molecules and molecular compounds. In this paper, the Mostar index is studied. It is presented the relationships between the Mostar index and other topological indices. Inequalities about some parameters and also Nordhaus-Gaddum-type results for the Mostar index are also presented.\"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132946832","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 regular and intra-regular Γ-semihypergroups","authors":"Safoora J. Ansari, K. Pawar, K. Hila","doi":"10.37193/cmi.2022.01.02","DOIUrl":"https://doi.org/10.37193/cmi.2022.01.02","url":null,"abstract":"\"In this paper we have investigated the intra-regular Γ-semihypergroup S and presented its characterizations while exploring properties of Γ-hyperideals of S. We have also studied the Γ-semihypergroup which is both regular and intra-regular and proved some results in this regard. We have investigated converse of some results and provided counterexamples as well.\"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128078881","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 extensions of pseudo-valuations on BCK algebras","authors":"D. Busneag, D. Piciu, M. Istrata","doi":"10.37193/cmi.2022.01.04","DOIUrl":"https://doi.org/10.37193/cmi.2022.01.04","url":null,"abstract":"\"In this paper we define a pseudo-valuation on a BCK algebra (A,→, 1) as a real-valued function v : A → R satisfying v(1) = 0 and v(x → y) ≥ v(y) − v(x), for every x, y ∈ A ; v is called a valuation if x = 1 whenever v(x) = 0. We prove that every pseudo-valuation (valuation) v induces a pseudo-metric (metric) on A defined by dv(x, y) = v(x → y) + v(y → x) for every x, y ∈ A, where → is uniformly continuous in both variables. The aim of this paper is to provide several theorems on extensions of pseudo-valuations (valuations) on BCK algebras. In this paper we define a pseudo-valuation on a BCK algebra (A,→, 1) as a real-valued function v : A → R satisfying v(1) = 0 and v(x → y) ≥ v(y) − v(x), for every x, y ∈ A ; v is called a valuation if x = 1 whenever v(x) = 0. We prove that every pseudo-valuation (valuation) v induces a pseudo-metric (metric) on A defined by dv(x, y) = v(x → y) + v(y → x) for every x, y ∈ A, where → is uniformly continuous in both variables. The aim of this paper is to provide several theorems on extensions of pseudo-valuations (valuations) on BCK algebras. In this paper we define a pseudo-valuation on a BCK algebra (A,→, 1) as a real-valued function v : A → R satisfying v(1) = 0 and v(x → y) ≥ v(y) − v(x), for every x, y ∈ A ; v is called a valuation if x = 1 whenever v(x) = 0. We prove that every pseudo-valuation (valuation) v induces a pseudo-metric (metric) on A defined by dv(x, y) = v(x → y) + v(y → x) for every x, y ∈ A, where → is uniformly continuous in both variables. The aim of this paper is to provide several theorems on extensions of pseudo-valuations (valuations) on BCK algebras.\"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"124 18","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113940076","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}
Mireya Cintora, Claudia Gutierrez, Roberto C. Soto, Bogdan D. Suceavă, A. Verdugo
{"title":"\"Exploring a Class of Substitutions and their Applications: Reflections on Teaching Foundations of Real Analysis\"","authors":"Mireya Cintora, Claudia Gutierrez, Roberto C. Soto, Bogdan D. Suceavă, A. Verdugo","doi":"10.37193/cmi.2022.01.13","DOIUrl":"https://doi.org/10.37193/cmi.2022.01.13","url":null,"abstract":"We are investigating a class of integrable functions which admit an integration process through elementary integration steps. We are using a class of natural $u$-substitutions given by linear bijections symmetrizing the interval of integration.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122052179","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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