Abstract According to Gauss-Lucas theorem, every convex set containing all the zeros of a polynomial also contains all its critical points. This result is of central importance in the geometry of critical points in the analytic theory of polynomials. In this paper, an extension of Gauss-Lucas theorem is obtained and as an application some generalizations of Bernstein-type polynomial inequalities are also established.
{"title":"Gauss Lucas theorem and Bernstein-type inequalities for polynomials","authors":"Liyaqat Ali, N. A. Rather, Suhail Gulzar","doi":"10.2478/ausm-2022-0013","DOIUrl":"https://doi.org/10.2478/ausm-2022-0013","url":null,"abstract":"Abstract According to Gauss-Lucas theorem, every convex set containing all the zeros of a polynomial also contains all its critical points. This result is of central importance in the geometry of critical points in the analytic theory of polynomials. In this paper, an extension of Gauss-Lucas theorem is obtained and as an application some generalizations of Bernstein-type polynomial inequalities are also established.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85932174","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}
Abstract In this paper, we define a distance d on the set ℳ of bivariate means. We show that (ℳ, d) is a bounded complete metric space which is not compact. Other algebraic and topological properties of (ℳ, d) are investigated as well.
{"title":"On a metric topology on the set of bivariate means","authors":"M. Raïssouli, Mohamed Chergui","doi":"10.2478/ausm-2022-0010","DOIUrl":"https://doi.org/10.2478/ausm-2022-0010","url":null,"abstract":"Abstract In this paper, we define a distance d on the set ℳ of bivariate means. We show that (ℳ, d) is a bounded complete metric space which is not compact. Other algebraic and topological properties of (ℳ, d) are investigated as well.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83927004","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}
Abstract This current work is presented to deal with the model of double diffusive convection in porous material with variable viscosity, such that the equations for convective fluid motion in a Brinkman type are analysed when the viscosity varies with temperature quadratically. Hence, we carefully find a priori bounds when the coe cients depend only on the geometry of the problem, initial data, and boundary data, where this shows the continuous dependence of the solution on changes in the viscosity. A convergence result is also showen when the variable viscosity is allowed to tend to a constant viscosity.
{"title":"Continuous dependence for double diffusive convection in a Brinkman model with variable viscosity","authors":"G. A. Meften, Ali Hasan Ali","doi":"10.2478/ausm-2022-0009","DOIUrl":"https://doi.org/10.2478/ausm-2022-0009","url":null,"abstract":"Abstract This current work is presented to deal with the model of double diffusive convection in porous material with variable viscosity, such that the equations for convective fluid motion in a Brinkman type are analysed when the viscosity varies with temperature quadratically. Hence, we carefully find a priori bounds when the coe cients depend only on the geometry of the problem, initial data, and boundary data, where this shows the continuous dependence of the solution on changes in the viscosity. A convergence result is also showen when the variable viscosity is allowed to tend to a constant viscosity.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82935961","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. Bouchentouf, Meriem Houalef, Abdelhak Guendouzi
Abstract This paper is concerned with the analysis of an infinite-capacity batch arrival multi-server queueing system with Bernoulli feedback, synchronous multiple and single working vacation policies, waiting servers, reneging and retention of reneged customers. The steady-state solution of the queueing system is obtained by using probability generating function (PGF). In addition, important performance measures of the queueing system are derived. Then, a cost model is formulated in order to carry out the parameter optimization using genetic algorithm (GA). Finally, numerical study is presented in which various system performance measures are evaluated based on supposed numerical values given to the system parameters.
{"title":"Analysis of a batch arrival multi-server queueing system with waiting servers, synchronous working vacations and impatient customers","authors":"A. Bouchentouf, Meriem Houalef, Abdelhak Guendouzi","doi":"10.2478/ausm-2022-0003","DOIUrl":"https://doi.org/10.2478/ausm-2022-0003","url":null,"abstract":"Abstract This paper is concerned with the analysis of an infinite-capacity batch arrival multi-server queueing system with Bernoulli feedback, synchronous multiple and single working vacation policies, waiting servers, reneging and retention of reneged customers. The steady-state solution of the queueing system is obtained by using probability generating function (PGF). In addition, important performance measures of the queueing system are derived. Then, a cost model is formulated in order to carry out the parameter optimization using genetic algorithm (GA). Finally, numerical study is presented in which various system performance measures are evaluated based on supposed numerical values given to the system parameters.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85093323","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}
Abstract We contribute to the development of equivalence of fixed point iterative sequences for multivalued mappings in modular function spaces, by proving the equivalence of convergence of implicit Mann, implicit Ishikawa, implicit Noor, implicit multistep iterative sequences for multivalued ρ− quasi-contractive-like mapppings in modular function spaces. An example is provided to support the applicability of the results. This work is complementary to equivalence results on normed and metric spaces in the literature.
{"title":"Fixed point theorems and equivalence results for classes of multivalued mappings in modular function spaces","authors":"H. Akewe, Adesanmi Alao Mogbademu, H. Olaoluwa","doi":"10.2478/ausm-2022-0001","DOIUrl":"https://doi.org/10.2478/ausm-2022-0001","url":null,"abstract":"Abstract We contribute to the development of equivalence of fixed point iterative sequences for multivalued mappings in modular function spaces, by proving the equivalence of convergence of implicit Mann, implicit Ishikawa, implicit Noor, implicit multistep iterative sequences for multivalued ρ− quasi-contractive-like mapppings in modular function spaces. An example is provided to support the applicability of the results. This work is complementary to equivalence results on normed and metric spaces in the literature.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73613962","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}
Abstract The intention of this article is to introduce and characterise the concept of preopen sets and prelocally closed sets in Generalised Topology and Minimal structure spaces.
摘要本文的目的是在广义拓扑和极小结构空间中引入和刻画预开集和预局部闭集的概念。
{"title":"Preopen sets and prelocally closed sets in generalised topology and minimal structure spaces","authors":"Anjalu Albis Basumatary, D. Sarma, B. Tripathy","doi":"10.2478/ausm-2022-0002","DOIUrl":"https://doi.org/10.2478/ausm-2022-0002","url":null,"abstract":"Abstract The intention of this article is to introduce and characterise the concept of preopen sets and prelocally closed sets in Generalised Topology and Minimal structure spaces.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81562297","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}
Abstract This paper studies the existence of periodic solutions of a third order iterative differential equation. The main tool used here is Krasnoselskii-Burton’s fixed point theorem dealing with a sum of two mappings, one is a large contraction and the other is compact.
{"title":"Study of periodic solutions for third-order iterative differential equations via Krasnoselskii-Burton’s theorem","authors":"Abderrahim Guerfi, A. Ardjouni","doi":"10.2478/ausm-2022-0005","DOIUrl":"https://doi.org/10.2478/ausm-2022-0005","url":null,"abstract":"Abstract This paper studies the existence of periodic solutions of a third order iterative differential equation. The main tool used here is Krasnoselskii-Burton’s fixed point theorem dealing with a sum of two mappings, one is a large contraction and the other is compact.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73233911","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}
Abstract This article shows the existence and multiplicity of weak solutions for the singular subelliptic system on the Heisenberg group { -Δℍnu+a(ξ)u(| z |4+t2)12=λFu(ξ,u,v)in Ω,-Δℍnv+b(ξ)v(| z |4+t2)12=λFv(ξ,u,v)in Ω,u=v=0on ∂Ω. left{ {matrix{ { - {Delta _{{mathbb{H}^n}}}u + aleft( xi right){u over {{{left( {{{left| z right|}^4} + {t^2}} right)}^{{1 over 2}}}}} = lambda {F_u}left( {xi ,u,v} right)} hfill & {in,,,Omega ,} hfill cr { - {Delta _{{mathbb{H}^n}}}v + bleft( xi right){v over {{{left( {{{left| z right|}^4} + {t^2}} right)}^{{1 over 2}}}}} = lambda {F_v}left( {xi ,u,v} right)} hfill & {in,,,Omega ,} hfill cr {u = v = 0} hfill & {on,,partial Omega .} hfill cr } } right. The approach is based on variational methods.
摘要本文证明了奇异次椭圆型系统在Heisenberg群{-Δ nu+a(ξ)u(| z |4+t2)12=λFu(ξ，u,v)在Ω，-Δ nv+b(ξ)v(| z |4+t2)12=λFv(ξ，u,v)在Ω，u=v=0on∂Ω上弱解的存在性和多重性。}} 对。该方法基于变分方法。
{"title":"Existence results of infinitely many weak solutions of a singular subelliptic system on the Heisenberg group","authors":"S. Heidari, A. Razani","doi":"10.2478/ausm-2022-0006","DOIUrl":"https://doi.org/10.2478/ausm-2022-0006","url":null,"abstract":"Abstract This article shows the existence and multiplicity of weak solutions for the singular subelliptic system on the Heisenberg group { -Δℍnu+a(ξ)u(| z |4+t2)12=λFu(ξ,u,v)in Ω,-Δℍnv+b(ξ)v(| z |4+t2)12=λFv(ξ,u,v)in Ω,u=v=0on ∂Ω. left{ {matrix{ { - {Delta _{{mathbb{H}^n}}}u + aleft( xi right){u over {{{left( {{{left| z right|}^4} + {t^2}} right)}^{{1 over 2}}}}} = lambda {F_u}left( {xi ,u,v} right)} hfill & {in,,,Omega ,} hfill cr { - {Delta _{{mathbb{H}^n}}}v + bleft( xi right){v over {{{left( {{{left| z right|}^4} + {t^2}} right)}^{{1 over 2}}}}} = lambda {F_v}left( {xi ,u,v} right)} hfill & {in,,,Omega ,} hfill cr {u = v = 0} hfill & {on,,partial Omega .} hfill cr } } right. The approach is based on variational methods.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74052069","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}
Abstract This paper aims to show how some standard general results can be used to uncover the spectral theory of tridiagonal and related matrices more elegantly and simply than existing approaches. As a typical example, we apply the theory to the special tridiagonal matrices in recent papers on orthogonal polynomials arising from Jordan blocks. Consequently, we find that the polynomials and spectral theory of the special matrices are expressible in terms of the Chebyshev polynomials of second kind, whose properties yield interesting results. For special cases, we obtain results in terms of the Fibonacci numbers and Legendre polynomials.
{"title":"On tridiagonal matrices associated with Jordan blocks","authors":"C. D. da Fonseca, V. Kowalenko","doi":"10.2478/ausm-2022-0004","DOIUrl":"https://doi.org/10.2478/ausm-2022-0004","url":null,"abstract":"Abstract This paper aims to show how some standard general results can be used to uncover the spectral theory of tridiagonal and related matrices more elegantly and simply than existing approaches. As a typical example, we apply the theory to the special tridiagonal matrices in recent papers on orthogonal polynomials arising from Jordan blocks. Consequently, we find that the polynomials and spectral theory of the special matrices are expressible in terms of the Chebyshev polynomials of second kind, whose properties yield interesting results. For special cases, we obtain results in terms of the Fibonacci numbers and Legendre polynomials.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81123048","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}
Abstract For given unit vectors x1, · · ·, xn of a real Banach space E, we define NA(ℒ(nE))(x1,…xn)={ T∈ℒ(nE):| T(x1,…xn) |=‖ T ‖=1 }, NAleft( {mathcal{L}left( {^nE} right)} right)left( {{x_1}, ldots {x_n}} right) = left{ {T in mathcal{L}left( {^nE} right):left| {Tleft( {{x_1}, ldots {x_n}} right)} right| = left| T right| = 1} right}, where ℒ(nE) denotes the Banach space of all continuous n-linear forms on E endowed with the norm ||T|| = sup||xk||=1,1≤k≤n |T(x1, . . ., xn)|. In this paper, we classify NA(ℒ(2l12))((x1, x2), (y1, y2)) for unit vectors (x1, x2), (y1, y2)∈ l12, where l12 = ℝ2 with the l1-norm.
{"title":"Norm attaining bilinear forms on the plane with the l1-norm","authors":"Sung Guen Kim","doi":"10.2478/ausm-2022-0008","DOIUrl":"https://doi.org/10.2478/ausm-2022-0008","url":null,"abstract":"Abstract For given unit vectors x1, · · ·, xn of a real Banach space E, we define NA(ℒ(nE))(x1,…xn)={ T∈ℒ(nE):| T(x1,…xn) |=‖ T ‖=1 }, NAleft( {mathcal{L}left( {^nE} right)} right)left( {{x_1}, ldots {x_n}} right) = left{ {T in mathcal{L}left( {^nE} right):left| {Tleft( {{x_1}, ldots {x_n}} right)} right| = left| T right| = 1} right}, where ℒ(nE) denotes the Banach space of all continuous n-linear forms on E endowed with the norm ||T|| = sup||xk||=1,1≤k≤n |T(x1, . . ., xn)|. In this paper, we classify NA(ℒ(2l12))((x1, x2), (y1, y2)) for unit vectors (x1, x2), (y1, y2)∈ l12, where l12 = ℝ2 with the l1-norm.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88021644","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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