In this paper, we give some recent and new results for some contraction mappings on O−complete metric-like space and also we give illustrative examples. At the end, we give an application to show the existence of a solution of a differential equation.
{"title":"Some recent and new fixed point results on orthogonal metric-like space","authors":"Özlem ACAR","doi":"10.33205/cma.1360402","DOIUrl":"https://doi.org/10.33205/cma.1360402","url":null,"abstract":"In this paper, we give some recent and new results for some contraction mappings on O−complete metric-like space and also we give illustrative examples. At the end, we give an application to show the existence of a solution of a differential equation.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135352804","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}
Extensions of a positive hermitian linear functional $omega$, defined on a dense *-subalgebra $mathfrak{A_{0}}$ of a topological *-algebra $mathfrak{A}[tau]$ are analyzed. It turns out that their maximal extension as linear functionals or hermitian linear functional are everywhere defined. The situation however changes deeply if one looks for positive extensions. The case of fully positive and widely positive extensions considered in [1] is rivisited from this point of view. Examples mostly taken from the theory of integration are discussed.
{"title":"Maximal extensions of a linear functional","authors":"Fabio BURDERİ, Camillo TRAPANI, Salvatore TRİOLO","doi":"10.33205/cma.1310238","DOIUrl":"https://doi.org/10.33205/cma.1310238","url":null,"abstract":"Extensions of a positive hermitian linear functional $omega$, defined on a dense *-subalgebra $mathfrak{A_{0}}$ of a topological *-algebra $mathfrak{A}[tau]$ are analyzed. It turns out that their maximal extension as linear functionals or hermitian linear functional are everywhere defined. The situation however changes deeply if one looks for positive extensions. The case of fully positive and widely positive extensions considered in [1] is rivisited from this point of view. Examples mostly taken from the theory of integration are discussed.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135485984","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 the work we estimate the $mathbb{L}^1$ norms of some special cosine and sine series used in studying fractional integrals.
在这项工作中，我们估计了一些用于研究分数积分的特殊余弦和正弦级数的$mathbb｛L｝^1$范数。
{"title":"Estimates of the norms of some cosine and sine series","authors":"J. Bustamante","doi":"10.33205/cma.1345440","DOIUrl":"https://doi.org/10.33205/cma.1345440","url":null,"abstract":"In the work we estimate the $mathbb{L}^1$ norms of some special cosine and sine series used in studying fractional integrals.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43817213","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}
V. Gutlyanski̇i̇, O. Nesmelova, V. Ryazanov, E. Yakubov
We study the semi-linear Beltrami equation $omega_{bar{z}}-mu(z) omega_z=sigma(z)q(omega(z))$ and show that it is closely related to the corresponding semi-linear equation of the form ${rm div} A(z)nabla,U(z)=G(z) Q(U(z)).$ Applying the theory of completely continuous operators by Ahlfors-Bers and Leray-Schauder, we prove existence of regular solutions both to the semi-linear Beltrami equation and to the given above semi-linear equation in the divergent form, see Theorems 1.1 and 5.2. We also derive their representation through solutions of the semi-linear Vekua type equations and generalized analytic functions with sources. Finally, we apply Theorem 5.2 for several model equations describing physical phenomena in anisotropic and inhomogeneous media.
{"title":"Toward the theory of semi-linear Beltrami equations","authors":"V. Gutlyanski̇i̇, O. Nesmelova, V. Ryazanov, E. Yakubov","doi":"10.33205/cma.1248692","DOIUrl":"https://doi.org/10.33205/cma.1248692","url":null,"abstract":"We study the semi-linear Beltrami equation $omega_{bar{z}}-mu(z) omega_z=sigma(z)q(omega(z))$ and show that it is closely related to the corresponding semi-linear equation of the form ${rm div} A(z)nabla,U(z)=G(z) Q(U(z)).$ Applying the theory of completely continuous operators by Ahlfors-Bers and Leray-Schauder, we prove existence of regular solutions both to the semi-linear Beltrami equation and to the given above semi-linear equation in the divergent form, see Theorems 1.1 and 5.2. We also derive their representation through solutions of the semi-linear Vekua type equations and generalized analytic functions with sources. Finally, we apply Theorem 5.2 for several model equations describing physical phenomena in anisotropic and inhomogeneous media.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48087745","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}
Bessel multipliers are operators defined from two Bessel sequences of elements of a Hilbert space and a complex sequence, and have frame multipliers as particular cases. In this paper an estimate of the spectral radius of a Bessel multiplier is provided involving the cross Gram operator of the two sequences. As an upshot, it is possible to individuate some regions of the complex plane where the spectrum of a multiplier of dual frames is contained.
{"title":"Estimate of the spectral radii of Bessel multipliers and consequences","authors":"R. Corso","doi":"10.33205/cma.1323956","DOIUrl":"https://doi.org/10.33205/cma.1323956","url":null,"abstract":"Bessel multipliers are operators defined from two Bessel sequences of elements of a Hilbert space and a complex sequence, and have frame multipliers as particular cases. In this paper an estimate of the spectral radius of a Bessel multiplier is provided involving the cross Gram operator of the two sequences. As an upshot, it is possible to individuate some regions of the complex plane where the spectrum of a multiplier of dual frames is contained.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42170073","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 $Omega$ be a bounded domain in $mathbb{R}^{n}$ with $C^{0,1}$ boundary, and let $d_{Omega}:Omegarightarrowmathbb{R}$ be the distance function $d_{Omega}left( xright) :=distleft( x,partialOmegaright) .$ Our aim in this paper is to study the existence and properties of principal eigenvalues of self-adjoint elliptic operators with weight function and singular potential, whose model problem is $-Delta u+bu=lambda mu$ in $Omega,$ $u=0$ on $partialOmega,$ $u>0$ in $Omega,$ where $b:Omega rightarrowmathbb{R}$ is a nonnegative function such that $d_{Omega}^{2}bin L^{infty}left( Omegaright) ,$ $m:Omegarightarrowmathbb{R}$ is a nonidentically zero function in $L^{infty}left( Omegaright) $ that may change sign, and the solutions are understood in weak sense.
{"title":"Principal eigenvalues of elliptic problems with singular potential and bounded weight function","authors":"T. Godoy","doi":"10.33205/cma.1272110","DOIUrl":"https://doi.org/10.33205/cma.1272110","url":null,"abstract":"Let $Omega$ be a bounded domain in $mathbb{R}^{n}$ with $C^{0,1}$ boundary, and let $d_{Omega}:Omegarightarrowmathbb{R}$ be the distance function $d_{Omega}left( xright) :=distleft( x,partialOmegaright) .$ Our aim in this paper is to study the existence and properties of principal eigenvalues of self-adjoint elliptic operators with weight function and singular potential, whose model problem is $-Delta u+bu=lambda mu$ in $Omega,$ $u=0$ on $partialOmega,$ $u>0$ in $Omega,$ where $b:Omega rightarrowmathbb{R}$ is a nonnegative function such that $d_{Omega}^{2}bin L^{infty}left( Omegaright) ,$ $m:Omegarightarrowmathbb{R}$ is a nonidentically zero function in $L^{infty}left( Omegaright) $ that may change sign, and the solutions are understood in weak sense.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46443705","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 we pose the $infty$-Laplace Equation as a Dirichlet Problem in a class of Grushin-type spaces whose vector fields are of the form begin{equation*} X_k(p):=sigma_k(p)frac{partial}{partial x_k} end{equation*} and $sigma_k$ is not a polynomial for indices $m+1 leq k leq n$. Solutions to the $infty$-Laplacian in the viscosity sense have been shown to exist and be unique in [3], when $sigma_k$ is a polynomial; we extend these results by exploiting the relationship between Grushin-type and Euclidean second-order jets and utilizing estimates on the viscosity derivatives of sub- and supersolutions in order to produce a comparison principle for semicontinuous functions.
本文将$infty$ -Laplace方程作为一类grushin型空间的Dirichlet问题，该类空间的向量场为begin{equation*} X_k(p):=sigma_k(p)frac{partial}{partial x_k} end{equation*}，且$sigma_k$不是指标$m+1 leq k leq n$的多项式。粘度意义上的$infty$ -拉普拉斯方程的解在[3]中是存在且唯一的，当$sigma_k$是多项式时;我们利用grushin型和欧几里得二阶射流之间的关系，并利用对亚解和超解的粘度导数的估计来推广这些结果，从而得出半连续函数的比较原理。
{"title":"Existence and uniqueness of viscosity solutions to the infinity Laplacian relative to a class of Grushin-type vector fields","authors":"Thomas Bieske, Zachary Forrest","doi":"10.33205/cma.1245581","DOIUrl":"https://doi.org/10.33205/cma.1245581","url":null,"abstract":"In this paper we pose the $infty$-Laplace Equation as a Dirichlet Problem in a class of Grushin-type spaces whose vector fields are of the form\u0000 begin{equation*}\u0000 X_k(p):=sigma_k(p)frac{partial}{partial x_k}\u0000 end{equation*}\u0000 and $sigma_k$ is not a polynomial for indices $m+1 leq k leq n$. Solutions to the $infty$-Laplacian in the viscosity sense have been shown to exist and be unique in [3], when $sigma_k$ is a polynomial; we extend these results by exploiting the relationship between Grushin-type and Euclidean second-order jets and utilizing estimates on the viscosity derivatives of sub- and supersolutions in order to produce a comparison principle for semicontinuous functions.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43740791","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 prove the unique existence of the functions $r_n$ $(n=1,2,ldots )$ on $[0,1]$ such that the corresponding sequence of King operators approximates each continuous function on $[0,1]$ and preserves the functions $e_0(x)=1$ and $e_j(x)=x^j$, where $jin{ 2,3,ldots}$ is fixed. We establish the essential properties of $r_n$, and the rate of convergence of the new sequence of King operators will be estimated by the usual modulus of continuity. Finally, we show that the introduced operators are not polynomial and we obtain quantitative Voronovskaja type theorems for these operators.
{"title":"King operators which preserve $x^j$","authors":"Z. Finta","doi":"10.33205/cma.1259505","DOIUrl":"https://doi.org/10.33205/cma.1259505","url":null,"abstract":"We prove the unique existence of the functions $r_n$ $(n=1,2,ldots )$ on $[0,1]$ such that the corresponding sequence of King operators approximates each continuous function on $[0,1]$ and preserves the functions $e_0(x)=1$ and $e_j(x)=x^j$, where $jin{ 2,3,ldots}$ is fixed. We establish the essential properties of $r_n$, and the rate of convergence of the new sequence of King operators will be estimated by the usual modulus of continuity. Finally, we show that the introduced operators are not polynomial and we obtain quantitative Voronovskaja type theorems for these operators.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47398396","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 is to provide a generalization of Carleson's Theorem on interpolating sequences when dealing with a sequence in the open unit ball of a Hilbert space. Precisely, we interpolate a sequence by a function belonging to a weighted Bergman space of infinite order on a unit Hilbert ball and we furnish explicitly the upper bound corresponding to the interpolation constant.
{"title":"On an interpolation sequence for a weighted Bergman space on a Hilbert unit ball","authors":"Mohammed EL AIDI","doi":"10.33205/cma.1240126","DOIUrl":"https://doi.org/10.33205/cma.1240126","url":null,"abstract":"The purpose is to provide a generalization of Carleson's Theorem on interpolating sequences when dealing with a sequence in the open unit ball of a Hilbert space. Precisely, we interpolate a sequence by a function belonging to a weighted Bergman space of infinite order on a unit Hilbert ball and we furnish explicitly the upper bound corresponding to the interpolation constant.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46335279","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}
Mohammad KARİMNEJAD ESFAHANİ, Stefano DE MARCHI, Francesco MARCHETTİ
Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these functions are therefore of great importance. In this paper, we design a moving least-squares approach for scattered data approximation that incorporates the discontinuities in the weight functions. The idea is to control the influence of the data sites on the approximant, not only with regards to their distance from the evaluation point, but also with respect to the discontinuity of the underlying function. We also provide an error estimate on a suitable piecewise Sobolev Space. The numerical experiments are in compliance with the convergence rate derived theoretically.
{"title":"Moving least squares approximation using variably scaled discontinuous weight function","authors":"Mohammad KARİMNEJAD ESFAHANİ, Stefano DE MARCHI, Francesco MARCHETTİ","doi":"10.33205/cma.1247239","DOIUrl":"https://doi.org/10.33205/cma.1247239","url":null,"abstract":"Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these functions are therefore of great importance. In this paper, we design a moving least-squares approach for scattered data approximation that incorporates the discontinuities in the weight functions. The idea is to control the influence of the data sites on the approximant, not only with regards to their distance from the evaluation point, but also with respect to the discontinuity of the underlying function. We also provide an error estimate on a suitable piecewise Sobolev Space. The numerical experiments are in compliance with the convergence rate derived theoretically.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135598694","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：