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Approximating an advanced multi-dimensional reciprocal-quadratic mapping via a fixed point approach 用不动点法逼近一种先进的多维往复式二次映射
IF 0.5
Boletim Sociedade Paranaense de Matematica Pub Date : 2022-12-28 DOI: 10.5269/bspm.62943
B. S. Senthil Kumar, H. Dutta, S. Sabarinathan
{"title":"Approximating an advanced multi-dimensional reciprocal-quadratic mapping via a fixed point approach","authors":"B. S. Senthil Kumar, H. Dutta, S. Sabarinathan","doi":"10.5269/bspm.62943","DOIUrl":"https://doi.org/10.5269/bspm.62943","url":null,"abstract":"There are many results on stability of various forms of functional equations available in the theory of functional equations. The intention of this paper is to introduce an advanced and a new multi-dimensional reciprocal-quadratic functional equation involving $p>1$ variables. It is interesting to note that it has two different solutions, namely, quadratic and multiplicative inverse quadratic functions. We solve its various stability problems in the setting of non-zero real numbers and non-Archimedean fields via fixed point approach.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42159813","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}
引用次数: 0
The infimum eigenvalue for degenerate p(x)-biharmonic operator with the Hardy potentiel 具有Hardy电位的退化p(x)-双调和算子的最小特征值
IF 0.5
Boletim Sociedade Paranaense de Matematica Pub Date : 2022-12-28 DOI: 10.5269/bspm.62754
Adnan Belakhdar, H. Belaouidel, Mohammed Filali, N. Tsouli
{"title":"The infimum eigenvalue for degenerate p(x)-biharmonic operator with the Hardy potentiel","authors":"Adnan Belakhdar, H. Belaouidel, Mohammed Filali, N. Tsouli","doi":"10.5269/bspm.62754","DOIUrl":"https://doi.org/10.5269/bspm.62754","url":null,"abstract":"The aim of this article is to study the existence of at least one unbounded nondecreasing sequence of nonnegative eigenvalues (λk)k≥1 for a class of elliptic Navier boundary value problems involving the degenerate p(·)-biharmonic operator with q(x)-Hardy inequality by using the variational technique based on the Ljusternik-Schnirelmann theory on C1-manifolds and the theory of the variable exponent Lebesgue spaces. Also, we obtain the positivity of the infimum eigenvalue for the problem.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42527446","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}
引用次数: 0
Solving fuzzy fractional Atangana-Baleanu differential equation using Adams-Bashforth-Moulton method 用Adams-Bashforth-Moulton方法求解模糊分数阶Atangana-Baleanu微分方程
IF 0.5
Boletim Sociedade Paranaense de Matematica Pub Date : 2022-12-28 DOI: 10.5269/bspm.63335
S. Melliani, Fouziya Zamtain, M. Elomari, L. S. Chadli
{"title":"Solving fuzzy fractional Atangana-Baleanu differential equation using Adams-Bashforth-Moulton method","authors":"S. Melliani, Fouziya Zamtain, M. Elomari, L. S. Chadli","doi":"10.5269/bspm.63335","DOIUrl":"https://doi.org/10.5269/bspm.63335","url":null,"abstract":"This work is concerned with the numerical study of the fuzzy fractional equation involving the Atangana-Baleanu derivative in the sense of Caputo. We are going to apply the Adams Bashforth Moulton method to the equation concerned, which is an interconnection between the Lagrange approximation and the trapezoidal rule. We achieved this work by giving examples that illustrate this method.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41415019","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}
引用次数: 0
On the solution of evolution p(.)-Bilaplace equation with variable 关于变量演化p（.）-Bilaplace方程的解
IF 0.5
Boletim Sociedade Paranaense de Matematica Pub Date : 2022-12-28 DOI: 10.5269/bspm.62640
A. Chaoui, Manal Djaghout
{"title":"On the solution of evolution p(.)-Bilaplace equation with variable","authors":"A. Chaoui, Manal Djaghout","doi":"10.5269/bspm.62640","DOIUrl":"https://doi.org/10.5269/bspm.62640","url":null,"abstract":"A high-order parabolic p(.)-Bilaplace equation with variable exponent is studied. The well-posedness at each time step of the problem in suitable Lebesgue Sobolev spaces with variable exponent with the help of nonlinear monotone operators theory is investigated. The solvability of the proposed problem as well as some regulrarity results are shown using Roth-Galerkin method .","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49540297","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}
引用次数: 0
Local properties of fourier series via deferred Riesz mean 递延Riesz均值傅里叶级数的局部性质
IF 0.5
Boletim Sociedade Paranaense de Matematica Pub Date : 2022-12-28 DOI: 10.5269/bspm.62309
P. Pattanaik, S. K. Paikray, Biplab Kumar Rath
{"title":"Local properties of fourier series via deferred Riesz mean","authors":"P. Pattanaik, S. K. Paikray, Biplab Kumar Rath","doi":"10.5269/bspm.62309","DOIUrl":"https://doi.org/10.5269/bspm.62309","url":null,"abstract":"The convergence of Fourier series of a function at a point depends upon the behaviour of the function in the neighborhood of that point, and it leads to the local property of Fourier series. In the proposed work, we introduce and study the absolute convergence of the deferred Riesz summability mean, and accordingly establish a new theorem on the local property of a factored Fourier series. We also suggest a direction for future researches on this subject, which are based upon the local properties of the Fourier series via basic notions of statistical absolute convergence.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46718701","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}
引用次数: 0
Weak solution to p(x)-Kirchoff type problems under no-flux boundary condition by topological degree 无通量边界条件下p(x)-Kirchoff型问题的拓扑度弱解
IF 0.5
Boletim Sociedade Paranaense de Matematica Pub Date : 2022-12-28 DOI: 10.5269/bspm.63341
Soukaina Yacini, C. Allalou, K. Hilal
{"title":"Weak solution to p(x)-Kirchoff type problems under no-flux boundary condition by topological degree","authors":"Soukaina Yacini, C. Allalou, K. Hilal","doi":"10.5269/bspm.63341","DOIUrl":"https://doi.org/10.5269/bspm.63341","url":null,"abstract":"This paper is concerned with the existence of weak solutions of $p(x)$-Kirchhoff type problems with no-flux boundary condition. Our technical approach is based on topological degre methods of Berkovits.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46049989","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}
引用次数: 1
Relative uniform convergence of double sequence of positive linear functions defined by Orlicz function Orlicz函数定义的正线性函数二重序列的相对一致收敛性
IF 0.5
Boletim Sociedade Paranaense de Matematica Pub Date : 2022-12-28 DOI: 10.5269/bspm.62715
Kshetrimayum Renubebeta Devi, B. Tripathy
{"title":"Relative uniform convergence of double sequence of positive linear functions defined by Orlicz function","authors":"Kshetrimayum Renubebeta Devi, B. Tripathy","doi":"10.5269/bspm.62715","DOIUrl":"https://doi.org/10.5269/bspm.62715","url":null,"abstract":"In this article, we introduce the notion of relative uniform convergence of double sequence of positive linear functions defined by using Orlicz function. We also introduce different classes of relative uniform convergence sequence of functions and discuss their algebraic and topological properties.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45660999","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}
引用次数: 0
Weak structures on texture spaces 纹理空间上的弱结构
IF 0.5
Boletim Sociedade Paranaense de Matematica Pub Date : 2022-12-28 DOI: 10.5269/bspm.62294
S. Dost
{"title":"Weak structures on texture spaces","authors":"S. Dost","doi":"10.5269/bspm.62294","DOIUrl":"https://doi.org/10.5269/bspm.62294","url":null,"abstract":"The purpose of this paper is to introduce and study weak structure on texture spaces. In this context, the notion of weak semi-open sets and weak bicontinuity are defined in weak distructure texture spaces, and is presented some characterization.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43129242","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}
引用次数: 0
On monogenity of certain pure number fields defined by $x^{2^rcdot7^s}-m$ 关于由x^{2^rcdot7^s}-m$定义的纯数域的单性
IF 0.5
Boletim Sociedade Paranaense de Matematica Pub Date : 2022-12-28 DOI: 10.5269/bspm.62352
L. El Fadil, O. Kchit
{"title":"On monogenity of certain pure number fields defined by $x^{2^rcdot7^s}-m$","authors":"L. El Fadil, O. Kchit","doi":"10.5269/bspm.62352","DOIUrl":"https://doi.org/10.5269/bspm.62352","url":null,"abstract":"Let $K$ be a pure number field generated by a complex root of a monic irreducible polynomial $F(x)=x^{2^rcdot7^s}-min mathbb{Z}[x]$, where $mneq pm 1$ is a square free integer, $r$ and $s$ are two positive integers. In this paper, we study the monogenity of $K$. We prove that if $mnotequiv 1md{4}$ and $overline{m}notin{pm overline{1},pm overline{18},pm overline{19}} md{49}$, then $K$ is monogenic. But if $rgeq 2$ and $mequiv 1md{16}$ or $sgeq 3$, $overline{m}in{ overline{1}, overline{18}, -overline{19}} md{49}$, and $nu_7(m^6-1)geq 4$, then $K$ is not monogenic. Some illustrating examples are given at the end of the paper.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47977166","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}
引用次数: 0
Numerical solution of non-linear Volterra integral equation of the first kind 第一类非线性Volterra积分方程的数值解
IF 0.5
Boletim Sociedade Paranaense de Matematica Pub Date : 2022-12-28 DOI: 10.5269/bspm.63205
Boutheina Tair, M. Ghiat, Hmaza Guebbai, Mohamed Zine Aissaoui
{"title":"Numerical solution of non-linear Volterra integral equation of the first kind","authors":"Boutheina Tair, M. Ghiat, Hmaza Guebbai, Mohamed Zine Aissaoui","doi":"10.5269/bspm.63205","DOIUrl":"https://doi.org/10.5269/bspm.63205","url":null,"abstract":"In this paper, we focus on the numerical solution of a nonlinear Volterra equation of the first kind. The existence and uniqueness of the exact solution is ensured under a necessary condition which we present next. We develop a numerical method based on two essential parts which are linearization and discretization. We start with the discretization of the equations using the concept of Nystrom's method and for the linearization we apply Newton's method. We present theorems that show the convergence of the proposed method. At the end, numerical  examples are presented to show the eficiency of our method.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44890834","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}
引用次数: 0
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