In this manuscript, we provide some new results for the existence of fixed points for a certain contractive condition of Geraghty type in the setting of partially ordered $G$-metric space. Also, we provide an example to illustrate the usability of results. Our results generalize or extend many well known results in the literature.
{"title":"Existence of fixed points in G-metric spaces","authors":"V. Chary, G. Reddy, D. S. Chary, S. Radenović","doi":"10.5269/bspm.50822","DOIUrl":"https://doi.org/10.5269/bspm.50822","url":null,"abstract":"In this manuscript, we provide some new results for the existence of fixed points for a certain contractive condition of Geraghty type in the setting of partially ordered $G$-metric space. Also, we provide an example to illustrate the usability of results. Our results generalize or extend many well known results in the literature.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45917618","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}
This investigation comprises the continuation of creative research in Discrete Mathematics presented in previous papers on algebras in general, regarding the utilization of graphs to contemplate the specific instance of graphicable algebras, which form a subset of evolution algebras. Evolution algebras are especially fascinating since they are intrinsically connected with other Mathematical fields, for example, grouptheory, stochastics processes and dynamical systems. Depiction on primeness of particular type of graphicable and subgraphicable algebras is described in view of the newline of research initiated previously by some of the authors.
{"title":"Certain types of ladder prime graphicable algebras","authors":"Karamthot Jayalakshmi, R. A. Lakshmi","doi":"10.5269/bspm.52700","DOIUrl":"https://doi.org/10.5269/bspm.52700","url":null,"abstract":"This investigation comprises the continuation of creative research in Discrete Mathematics presented in previous papers on algebras in general, regarding the utilization of graphs to contemplate the specific instance of graphicable algebras, which form a subset of evolution algebras. Evolution algebras are especially fascinating since they are intrinsically connected with other Mathematical fields, for example, grouptheory, stochastics processes and dynamical systems. Depiction on primeness of particular type of graphicable and subgraphicable algebras is described in view of the newline of research initiated previously by some of the authors.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45547851","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}
This article introduces the concepts of somewhat G-precontinuous mapping and somewhat G-preopen mappings. Using these notions, some examples and few interesting properties of those mappings are discussed by means of grill topological spaces.
{"title":"Somewhat precontinuous mappings via grill","authors":"A. Swaminathan, Sankari M","doi":"10.5269/bspm.51504","DOIUrl":"https://doi.org/10.5269/bspm.51504","url":null,"abstract":"This article introduces the concepts of somewhat G-precontinuous mapping and somewhat G-preopen mappings. Using these notions, some examples and few interesting properties of those mappings are discussed by means of grill topological spaces.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43279564","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 adapt strong θ−pre-continuity into fuzzy soft topology and investigate its properties. Also, the relations with the other types of continuities in fuzzy soft topological spaces are analized. Moreover, we give some new definitions.
{"title":"A note on strong form of fuzzy soft pre-continuity","authors":"H. Cakalli, A. Acikgoz, F. Esenbel","doi":"10.5269/bspm.50970","DOIUrl":"https://doi.org/10.5269/bspm.50970","url":null,"abstract":"We adapt strong θ−pre-continuity into fuzzy soft topology and investigate its properties. Also, the relations with the other types of continuities in fuzzy soft topological spaces are analized. Moreover, we give some new definitions.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45070766","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}
Moricz [Analysis (Munich) 18(1) (1998), 1-8] characterized summability (C,1) of integrals by convergence of another integral. In this work, we extend this result to logarithmic summability (L,1) of integrals.
{"title":"On the logarithmic summability $(L,1)$ of integrals on $[1,infty)$","authors":"Gökşen Fındık, Ibrahim Çanak","doi":"10.5269/bspm.50824","DOIUrl":"https://doi.org/10.5269/bspm.50824","url":null,"abstract":"Moricz [Analysis (Munich) 18(1) (1998), 1-8] characterized summability (C,1) of integrals by convergence of another integral. In this work, we extend this result to logarithmic summability (L,1) of integrals.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46809702","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 main aim of this article is to find the matrix recurrence relation and shift operators for the Gould-Hopper-Laguerre-Appell matrix polynomials. The matrix differential, matrix integro-differential and matrix partial differential equations are derived for these polynomials via factorization method. Certain examples are constructed in order to illustrate the applications of the results.
{"title":"Differential equations for certain hybrid special matrix polynomials","authors":"Tabinda Nahid, Subuhi Khan","doi":"10.5269/bspm.52758","DOIUrl":"https://doi.org/10.5269/bspm.52758","url":null,"abstract":"The main aim of this article is to find the matrix recurrence relation and shift operators for the Gould-Hopper-Laguerre-Appell matrix polynomials. The matrix differential, matrix integro-differential and matrix partial differential equations are derived for these polynomials via factorization method. Certain examples are constructed in order to illustrate the applications of the results.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46792829","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}
Let $R$ be a commutative ring with unit. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$, there is an ideal $I$ of $R$ such that $N=IM$. $M$ is called also a CF-module if there is some ideals $I_1,...,I_n$ of $R$ such that $M simeq R/I_1 bigoplus R/I_2 bigoplus ... bigoplus R/I_n$ and $I_1 subseteq I_2 subseteq ... subseteq I_n$. In this paper, we use some new results about $mu_R(M)$ the minimal number of generators of $M$ to show that a finitely generated multiplication module is a CF-module if and only if it is a cyclic module.
{"title":"The canonical form of multiplication modules","authors":"B. Boudine, Charkani Mohammed Elhassani","doi":"10.5269/bspm.52858","DOIUrl":"https://doi.org/10.5269/bspm.52858","url":null,"abstract":"Let $R$ be a commutative ring with unit. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$, there is an ideal $I$ of $R$ such that $N=IM$. $M$ is called also a CF-module if there is some ideals $I_1,...,I_n$ of $R$ such that $M simeq R/I_1 bigoplus R/I_2 bigoplus ... bigoplus R/I_n$ and $I_1 subseteq I_2 subseteq ... subseteq I_n$. In this paper, we use some new results about $mu_R(M)$ the minimal number of generators of $M$ to show that a finitely generated multiplication module is a CF-module if and only if it is a cyclic module.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41449852","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}
Let $K=Q(sqrt{d})$ be a quadratic field with discriminant $d$. It is shown that $sumlimits_{(frac{d}{p})=+1,_{p~ prime}}frac{1}{p}$ and $sumlimits_{(frac{d}{q})=-1,_{q~ prime}}frac{1}{q}$ are both divergent. Two different approaches are given to show the divergence: one using the Dedekind Zeta function and the other by Tauberian methods. It is shown that these two divergences are equivalent. It is shown that the divergence is equivalent to $L_{d}(1)neq 0$(de la Vall'{e}e Poussin's Theorem).We prove that the series $sumlimits_{(frac{d}{p})=+1,_{p~ prime}}frac{1}{p^{s}}$ and $sumlimits_{(frac{d}{q})=-1,_{q~ prime}}frac{1}{q^{s}}$ have singularities on all the imaginary axis(analogue of Landau-Walfisz theorem)
设$K=Q（sqrt｛d｝）$是具有判别式$d$的二次域。结果表明，$sumlimits_{（frac｛d｝｛p｝）=+1，_{p~prime｝｝frac{1｝{p｝$和$sumlimits_{。给出了两种不同的方法来显示分歧：一种使用Dedekind-Zeta函数，另一种使用Tauberian方法。结果表明，这两个发散是等价的。结果表明，散度等价于$L_｛d｝（1）neq0$（de la Vall）{e}ePoussin定理）。我们证明了序列$sumlimits_{（frac｛d｝｛p｝）=+1，_{p~素数｝｝frac{1｝｛p^｛s｝$和$sumlimits_{q~素数}｝frag｛1｝{q^｛s｝｝$在所有虚轴上都具有奇点（类似于Landau-Wallfisz定理）
{"title":"On the divergence of two subseries $ldots$] {on the divergence of two subseries of $sumfrac{1}{p}$, and theorems of de La Vall'{e}e Poussin and Landau-Walfis","authors":"G. Reddy, S. Rau, B. Uma","doi":"10.5269/bspm.50820","DOIUrl":"https://doi.org/10.5269/bspm.50820","url":null,"abstract":"Let $K=Q(sqrt{d})$ be a quadratic field with discriminant $d$. It is shown that $sumlimits_{(frac{d}{p})=+1,_{p~ prime}}frac{1}{p}$ and $sumlimits_{(frac{d}{q})=-1,_{q~ prime}}frac{1}{q}$ are both divergent. Two different approaches are given to show the divergence: one using the Dedekind Zeta function and the other by Tauberian methods. It is shown that these two divergences are equivalent. It is shown that the divergence is equivalent to $L_{d}(1)neq 0$(de la Vall'{e}e Poussin's Theorem).We prove that the series $sumlimits_{(frac{d}{p})=+1,_{p~ prime}}frac{1}{p^{s}}$ and $sumlimits_{(frac{d}{q})=-1,_{q~ prime}}frac{1}{q^{s}}$ have singularities on all the imaginary axis(analogue of Landau-Walfisz theorem)","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41934054","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, using a modulus function we generalize the concepts of ∆m−lacunary statistical convergence and ∆m−lacunary strongly convergence (m ∈ N) to ∆α−lacunary statistical convergence of order β with the fractional order of α and ∆α−lacunary strongly convergence of order β with the fractional order of α ( where 0 < β ≤ 1 and α be a fractional order).
{"title":"Generalized lacunary statistical convergence of order β of difference sequences of fractional order","authors":"N. D. Aral","doi":"10.5269/bspm.50848","DOIUrl":"https://doi.org/10.5269/bspm.50848","url":null,"abstract":"\u0000 \u0000 \u0000In this paper, using a modulus function we generalize the concepts of ∆m−lacunary statistical convergence and ∆m−lacunary strongly convergence (m ∈ N) to ∆α−lacunary statistical convergence of order β with the fractional order of α and ∆α−lacunary strongly convergence of order β with the fractional order of α ( where 0 < β ≤ 1 and α be a fractional order). \u0000 \u0000 \u0000","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48179399","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 aim of this paper is to characterize eta-Einstein N(k)-contact metric manifolds admits eta-Ricci soliton. Several consequences of this result are discussed. Beside these, we also study eta-Einstein N(k)-contact metric manifolds satisfying certain curvature conditions. Among others it is shown that such a manifold is either locally isometric to the Riemannian product En+1(0) Sn(4) or a Sasakian manifold. Finally, we construct an example to verify some results.
{"title":"On eta-Einstein N(k)-contact metric manifolds","authors":"S. Yadav, Xiaomin Chen","doi":"10.5269/bspm.46872","DOIUrl":"https://doi.org/10.5269/bspm.46872","url":null,"abstract":"The aim of this paper is to characterize eta-Einstein N(k)-contact metric manifolds admits eta-Ricci soliton. Several consequences of this result are discussed. Beside these, we also study eta-Einstein N(k)-contact metric manifolds satisfying certain curvature conditions. Among others it is shown that such a manifold is either locally isometric to the Riemannian product En+1(0) Sn(4) or a Sasakian manifold. Finally, we construct an example to verify some results.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43664559","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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