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.
{"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}
Adnan Belakhdar, H. Belaouidel, Mohammed Filali, N. Tsouli
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.
{"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}
S. Melliani, Fouziya Zamtain, M. Elomari, L. S. Chadli
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.
{"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}
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 .
{"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}
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.
{"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}
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.
{"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}
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.
{"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}
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.
{"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}
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.
设$K$是单不可约多项式$F（x）=x^｛2^rcdot7^s｝-minmathbb｛Z｝[x]$的复根生成的纯数域，其中$mneqpm1$是一个无平方整数，$r$和$s$是两个正整数。本文研究了$K$的单胚性。我们证明了如果$mnot equiv 1md｛4｝$和$overline｛m｝not in ｛pmoverline｝1｝，pmoverline｛18｝， pm overline{19｝｝md｛49｝$，那么$K$是单基因的。但是，如果$rgeq2$和$mequiv 1md｛16｝$或$sgeq3$、$overline｛m｝in ｛overline｝1｝、overline{18｝、-overline{19｝｝md｛49｝$和$nu_7（m^6-1）geq4$，则$K$不是单基因的。文末给出了一些实例。
{"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}
Boutheina Tair, M. Ghiat, Hmaza Guebbai, Mohamed Zine Aissaoui
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.
{"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}
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