Abstract Two-dimensional biharmonic boundary-value problems are considered by the linear barycentric rational collocation method, and the unknown function is approximated by the barycentric rational polynomial. With the help of matrix form, the linear equations of the discrete biharmonic equation are changed into a matrix equation. From the convergence rate of barycentric rational polynomial, we present the convergence rate of linear barycentric rational collocation method for biharmonic equation. Finally, several numerical examples are provided to validate the theoretical analysis.
{"title":"Linear barycentric rational collocation method for solving biharmonic equation","authors":"Jin Li","doi":"10.1515/dema-2022-0151","DOIUrl":"https://doi.org/10.1515/dema-2022-0151","url":null,"abstract":"Abstract Two-dimensional biharmonic boundary-value problems are considered by the linear barycentric rational collocation method, and the unknown function is approximated by the barycentric rational polynomial. With the help of matrix form, the linear equations of the discrete biharmonic equation are changed into a matrix equation. From the convergence rate of barycentric rational polynomial, we present the convergence rate of linear barycentric rational collocation method for biharmonic equation. Finally, several numerical examples are provided to validate the theoretical analysis.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"587 - 603"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43978553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Let A Φ ( K ) {{mathbb{A}}}_{Phi }left({bf{K}}) be the Banach algebra of bounded Φ Phi -variation functions defined on a compact set K {bf{K}} in the complex plane, h h a function defined on K {bf{K}} , and M h {M}_{h} a multiplication operator induced by h h . In this article, we determine the conditions that h h must satisfy for M h {M}_{h} to be an operator that has closed range, finite rank or is compact. We also characterize the conditions that h h must satisfy for M h {M}_{h} to be a Fredholm operator.
设A Φ (K) {{mathbb{A}}} ＿ {Phi}left({bf{K}})是定义在紧集K上的有界Φ Phi变分函数的Banach代数{bf{K}}，h h是定义在K上的函数，M h {bf{K}}M＿h{是由h h引起的乘法算子。在本文中，我们确定了h h是闭值域、有限秩或紧的算子时}h{ h必须满足的条件。我们还描述了h h必须满足的条件，使M h M＿h}成为{Fredholm}算子。{}{}{}
{"title":"Multiplication operators on the Banach algebra of bounded Φ-variation functions on compact subsets of ℂ","authors":"M. Bracamonte, J. Ereú, L. Marchan","doi":"10.1515/dema-2022-0162","DOIUrl":"https://doi.org/10.1515/dema-2022-0162","url":null,"abstract":"Abstract Let A Φ ( K ) {{mathbb{A}}}_{Phi }left({bf{K}}) be the Banach algebra of bounded Φ Phi -variation functions defined on a compact set K {bf{K}} in the complex plane, h h a function defined on K {bf{K}} , and M h {M}_{h} a multiplication operator induced by h h . In this article, we determine the conditions that h h must satisfy for M h {M}_{h} to be an operator that has closed range, finite rank or is compact. We also characterize the conditions that h h must satisfy for M h {M}_{h} to be a Fredholm operator.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"760 - 771"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46259297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Rashid Jan, Asma Alharbi, S. Boulaaras, Sultan Alyobi, Zaryab Khan
Abstract In Sub-Saharan Africa, zoonotic diseases are the leading cause of sickness and mortality, yet preventing their spread has long been difficult. Vaccination initiatives have significantly reduced the frequency of zoonotic diseases mostly in African regions. Nonetheless, zoonotic illnesses continue to be a hazard to underdeveloped countries. Zoonotic infections are spread by direct contact, food, and water. We construct an epidemic model to understand zoonotic disease transmission phenomena. The model is examined using the fundamental results of fractional theory. The reproduction parameter ℛ 0 {{mathcal{ {mathcal R} }}}_{0} was obtained by inspecting the model’s steady states. The stability of the system’s steady states has been demonstrated. The system’s reproduction parameter is quantitatively explored by varying various input parameters. Furthermore, the presence and uniqueness of the solution of the proposed dynamics of zoonotic diseases have been demonstrated. Different simulations of the recommended zoonotic disease model with different input factors are performed to inspect the complex dynamics of zoonotic disease with the influence of various model factors. To establish effective prevention and control measures for the infection, we analyse dynamical behaviour of the system. Decreasing the fractional order θ theta can decrease the infection level significantly. Different factors for reducing zoonotic diseases were recommended to regional policymakers.
{"title":"A robust study of the transmission dynamics of zoonotic infection through non-integer derivative","authors":"Rashid Jan, Asma Alharbi, S. Boulaaras, Sultan Alyobi, Zaryab Khan","doi":"10.1515/dema-2022-0179","DOIUrl":"https://doi.org/10.1515/dema-2022-0179","url":null,"abstract":"Abstract In Sub-Saharan Africa, zoonotic diseases are the leading cause of sickness and mortality, yet preventing their spread has long been difficult. Vaccination initiatives have significantly reduced the frequency of zoonotic diseases mostly in African regions. Nonetheless, zoonotic illnesses continue to be a hazard to underdeveloped countries. Zoonotic infections are spread by direct contact, food, and water. We construct an epidemic model to understand zoonotic disease transmission phenomena. The model is examined using the fundamental results of fractional theory. The reproduction parameter ℛ 0 {{mathcal{ {mathcal R} }}}_{0} was obtained by inspecting the model’s steady states. The stability of the system’s steady states has been demonstrated. The system’s reproduction parameter is quantitatively explored by varying various input parameters. Furthermore, the presence and uniqueness of the solution of the proposed dynamics of zoonotic diseases have been demonstrated. Different simulations of the recommended zoonotic disease model with different input factors are performed to inspect the complex dynamics of zoonotic disease with the influence of various model factors. To establish effective prevention and control measures for the infection, we analyse dynamical behaviour of the system. Decreasing the fractional order θ theta can decrease the infection level significantly. Different factors for reducing zoonotic diseases were recommended to regional policymakers.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"922 - 938"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41764889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This article establishes an asymptotic behavior for the elasticity systems with nonlinear source and dissipative terms in a three-dimensional thin domain, which generalizes some previous works. We consider the limit when the thickness tends to zero, and we prove that the limit solution u ∗ {u}^{ast } is a solution of a two-dimensional boundary value problem with lower Tresca’s free-boundary conditions. Moreover, we obtain the weak Reynolds-type equation.
{"title":"Source term model for elasticity system with nonlinear dissipative term in a thin domain","authors":"M. Dilmi, M. Dilmi, S. Boulaaras, H. Benseridi","doi":"10.1515/dema-2022-0033","DOIUrl":"https://doi.org/10.1515/dema-2022-0033","url":null,"abstract":"Abstract This article establishes an asymptotic behavior for the elasticity systems with nonlinear source and dissipative terms in a three-dimensional thin domain, which generalizes some previous works. We consider the limit when the thickness tends to zero, and we prove that the limit solution u ∗ {u}^{ast } is a solution of a two-dimensional boundary value problem with lower Tresca’s free-boundary conditions. Moreover, we obtain the weak Reynolds-type equation.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"437 - 451"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43817728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Michael J. Catanzaro, Lee Przybylski, Eric S. Weber
Abstract We develop a method for calculating the persistence landscapes of affine fractals using the parameters of the corresponding transformations. Given an iterated function system of affine transformations that satisfies a certain compatibility condition, we prove that there exists an affine transformation acting on the space of persistence landscapes, which intertwines the action of the iterated function system. This latter affine transformation is a strict contraction and its unique fixed point is the persistence landscape of the affine fractal. We present several examples of the theory as well as confirm the main results through simulations.
{"title":"Persistence landscapes of affine fractals","authors":"Michael J. Catanzaro, Lee Przybylski, Eric S. Weber","doi":"10.1515/dema-2022-0015","DOIUrl":"https://doi.org/10.1515/dema-2022-0015","url":null,"abstract":"Abstract We develop a method for calculating the persistence landscapes of affine fractals using the parameters of the corresponding transformations. Given an iterated function system of affine transformations that satisfies a certain compatibility condition, we prove that there exists an affine transformation acting on the space of persistence landscapes, which intertwines the action of the iterated function system. This latter affine transformation is a strict contraction and its unique fixed point is the persistence landscape of the affine fractal. We present several examples of the theory as well as confirm the main results through simulations.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"163 - 192"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43879780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
N. Mehmood, I. Khan, Muhammad Ayyaz Nawaz, Niaz Ahmad
Abstract In this article, fixed point results for self-mappings in the setting of two metrics satisfying F F -lipschitzian conditions of rational-type are proved, where F F is considered as a semi-Wardowski function with constant τ ∈ R tau in {mathbb{R}} instead of τ > 0 tau gt 0 . Two metrics have been considered, one as an incomplete while the other is orbitally complete. The mapping is taken to be orbitally continuous from one metric to another. Some examples are provided to validate our results. For applications, we present existence results for the solutions of a new type of ABC-fractional boundary value problem.
{"title":"Existence results for ABC-fractional BVP via new fixed point results of F-Lipschitzian mappings","authors":"N. Mehmood, I. Khan, Muhammad Ayyaz Nawaz, Niaz Ahmad","doi":"10.1515/dema-2022-0028","DOIUrl":"https://doi.org/10.1515/dema-2022-0028","url":null,"abstract":"Abstract In this article, fixed point results for self-mappings in the setting of two metrics satisfying F F -lipschitzian conditions of rational-type are proved, where F F is considered as a semi-Wardowski function with constant τ ∈ R tau in {mathbb{R}} instead of τ > 0 tau gt 0 . Two metrics have been considered, one as an incomplete while the other is orbitally complete. The mapping is taken to be orbitally continuous from one metric to another. Some examples are provided to validate our results. For applications, we present existence results for the solutions of a new type of ABC-fractional boundary value problem.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"452 - 469"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48323763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The aim of this paper is to study existence and uniqueness of coupled fixed point for a family of self-mappings satisfying a new coupled implicit relation in a Hilbert space. We also prove well-posedness of a coupled fixed point problem.
{"title":"Coupled fixed point theorems under new coupled implicit relation in Hilbert spaces","authors":"Kyung Soo Kim","doi":"10.1515/dema-2022-0010","DOIUrl":"https://doi.org/10.1515/dema-2022-0010","url":null,"abstract":"Abstract The aim of this paper is to study existence and uniqueness of coupled fixed point for a family of self-mappings satisfying a new coupled implicit relation in a Hilbert space. We also prove well-posedness of a coupled fixed point problem.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"81 - 89"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46936642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Let Y Y be a random real response, which is subject to right censoring by another random variable C C . In this paper, we study the nonparametric local linear estimation of the conditional density of a scalar response variable and when the covariable takes values in a semi-metric space. Our main aim is to prove under some regularity conditions both the pointwise and the uniform almost-sure consistencies with convergence rates of the conditional density estimator related by this estimation procedure.
{"title":"Local linear approach: Conditional density estimate for functional and censored data","authors":"A. Benkhaled, Fethi Madani","doi":"10.1515/dema-2022-0018","DOIUrl":"https://doi.org/10.1515/dema-2022-0018","url":null,"abstract":"Abstract Let Y Y be a random real response, which is subject to right censoring by another random variable C C . In this paper, we study the nonparametric local linear estimation of the conditional density of a scalar response variable and when the covariable takes values in a semi-metric space. Our main aim is to prove under some regularity conditions both the pointwise and the uniform almost-sure consistencies with convergence rates of the conditional density estimator related by this estimation procedure.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"315 - 327"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41564505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper deals with weighted Lupaş post-quantum Bernstein blending functions and Bézier curves constructed with the help of bases via ( p , q ) left(p,q) -integers. These blending functions form normalized totally positive bases. Due to the rational nature of weighted Lupaş post-quantum Bézier curves and positive weights, they help in investigating from geometric point of view. Their degree elevation properties and de Casteljau algorithm have been studied. It has been shown that quadratic weighted Lupaş post-quantum Bézier curves can represent conic sections in two-dimensional plane. Graphical analysis has been presented to discuss geometric interpretation of weight and conic section representation by weighted Lupaş post-quantum Bézier curves. This new generalized weighted Lupaş post-quantum Bézier curve provides better approximation and flexibility to a particular control point as well as control polygon due to extra parameter p p and q q in comparison to classical rational Bézier curves, Lupaş q q -Bézier curves and weighted Lupaş q q -Bézier curves.
{"title":"Approximation of conic sections by weighted Lupaş post-quantum Bézier curves","authors":"Asif Khan, M. Iliyas, Khalid Khan, M. Mursaleen","doi":"10.1515/dema-2022-0016","DOIUrl":"https://doi.org/10.1515/dema-2022-0016","url":null,"abstract":"Abstract This paper deals with weighted Lupaş post-quantum Bernstein blending functions and Bézier curves constructed with the help of bases via ( p , q ) left(p,q) -integers. These blending functions form normalized totally positive bases. Due to the rational nature of weighted Lupaş post-quantum Bézier curves and positive weights, they help in investigating from geometric point of view. Their degree elevation properties and de Casteljau algorithm have been studied. It has been shown that quadratic weighted Lupaş post-quantum Bézier curves can represent conic sections in two-dimensional plane. Graphical analysis has been presented to discuss geometric interpretation of weight and conic section representation by weighted Lupaş post-quantum Bézier curves. This new generalized weighted Lupaş post-quantum Bézier curve provides better approximation and flexibility to a particular control point as well as control polygon due to extra parameter p p and q q in comparison to classical rational Bézier curves, Lupaş q q -Bézier curves and weighted Lupaş q q -Bézier curves.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"328 - 342"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42016737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper presents some variants of minimal point theorem together with corresponding variants of Ekeland variational principle. In the second part of this article, there is a discussion on Ekeland variational principle and minimal point theorem relative to it in uniform spaces. The aim of these series of important results is to highlight relations between them, some improvements and specific applications.
{"title":"Remarks on some variants of minimal point theorem and Ekeland variational principle with applications","authors":"I. Meghea, C. Stamin","doi":"10.1515/dema-2022-0024","DOIUrl":"https://doi.org/10.1515/dema-2022-0024","url":null,"abstract":"Abstract This paper presents some variants of minimal point theorem together with corresponding variants of Ekeland variational principle. In the second part of this article, there is a discussion on Ekeland variational principle and minimal point theorem relative to it in uniform spaces. The aim of these series of important results is to highlight relations between them, some improvements and specific applications.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"354 - 379"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46023757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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