Journal of Mathematical Analysis and Applications最新文献

{"title":"A general functional version of Grünbaum's inequality","authors":"David Alonso-Gutiérrez ,&nbsp;Francisco Marín Sola ,&nbsp;Javier Martín Goñi ,&nbsp;Jesús Yepes Nicolás","doi":"10.1016/j.jmaa.2024.129065","DOIUrl":"10.1016/j.jmaa.2024.129065","url":null,"abstract":"<div><div>A classical inequality by Grünbaum provides a sharp lower bound for the ratio <span><math><mrow><mi>vol</mi></mrow><mo>(</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo><mo>/</mo><mrow><mi>vol</mi></mrow><mo>(</mo><mi>K</mi><mo>)</mo></math></span>, where <span><math><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup></math></span> denotes the intersection of a convex body with non-empty interior <span><math><mi>K</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with a halfspace bounded by a hyperplane <em>H</em> passing through the centroid <span><math><mi>g</mi><mo>(</mo><mi>K</mi><mo>)</mo></math></span> of <em>K</em>.</div><div>In this paper we extend this result to the case in which the hyperplane <em>H</em> passes by any of the points lying in a whole uniparametric family of <em>r</em>-powered centroids associated to <em>K</em> (depending on a real parameter <span><math><mi>r</mi><mo>≥</mo><mn>0</mn></math></span>), by proving a more general functional result on concave functions.</div><div>The latter result further connects (and allows one to recover) various inequalities involving the centroid, such as a classical inequality (due to Minkowski and Radon) that relates the distance of <span><math><mi>g</mi><mo>(</mo><mi>K</mi><mo>)</mo></math></span> to a supporting hyperplane of <em>K</em>, or a result for volume sections of convex bodies proven independently by Makai Jr. &amp; Martini and Fradelizi.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 1","pages":"Article 129065"},"PeriodicalIF":1.2,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bounds for Turánians of sections for series of certain subclasses of the Fox-Wright functions","authors":"Khaled Mehrez ,&nbsp;Kamel Brahim","doi":"10.1016/j.jmaa.2024.129055","DOIUrl":"10.1016/j.jmaa.2024.129055","url":null,"abstract":"<div><div>In this paper, we establish new Turán type inequalities for sections of some class of functions related to the generalized hypergeometric functions (Fox-Wright functions). The main mathematical tools of some of the main results are based on some new integral representations for the sections of hypergeometric functions and some monotonicity criterion of quotient of gamma function.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 1","pages":"Article 129055"},"PeriodicalIF":1.2,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705432","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}

{"title":"Stability estimate for a time-dependent coefficient identification problem in parabolic equations","authors":"Nguyen Van Thang ,&nbsp;Nguyen Van Duc","doi":"10.1016/j.jmaa.2024.129054","DOIUrl":"10.1016/j.jmaa.2024.129054","url":null,"abstract":"<div><div>This paper establishes stability estimates for an inverse problem of identifying a time-dependent coefficient in parabolic equations using the Carleman estimate technique.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 1","pages":"Article 129054"},"PeriodicalIF":1.2,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705431","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}

{"title":"Fixed point theorems of semigroup of isometry mappings and α-nonexpansive mappings on weak⁎ compact convex sets","authors":"Abhishek,&nbsp;S. Rajesh","doi":"10.1016/j.jmaa.2024.129053","DOIUrl":"10.1016/j.jmaa.2024.129053","url":null,"abstract":"<div><div>A.T.-M. Lau raised the question “Does a nonempty weak^⁎ compact convex subset <em>X</em> of a dual Banach space <span><math><mi>B</mi><msup><mrow></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> have the fixed point property for a left reversible semigroup of nonexpansive mappings whenever <em>X</em> has the weak^⁎ normal structure?” Fendler et al. proved that a dual Banach space <span><math><mi>B</mi><msup><mrow></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> has the weak^⁎ fixed point property for a left reversible semigroup of nonexpansive mappings in the presence of the asymptotic center property. In this paper, we prove that a left reversible semigroup of isometry mappings has a common fixed point in the Chebyshev center of <em>X</em> whenever <em>X</em> is a nonempty weak^⁎ compact convex subset of a dual Banach space <span><math><mi>B</mi><msup><mrow></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> and <span><math><mi>B</mi><msup><mrow></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> has the asymptotic center property. In 2010, A.T.-M. Lau et al. proved that a group <span><math><mi>G</mi></math></span> of isometric self-maps on a weak^⁎ compact convex subset <em>X</em> of a dual Banach space <span><math><mi>B</mi><msup><mrow></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> has a common fixed point in <em>X</em> whenever <em>X</em> has the weak^⁎ normal structure. In this paper, we prove that a group <span><math><mi>G</mi></math></span> of isometry mappings from <em>X</em> into itself has a common fixed point in the Chebyshev center of <em>X</em>. Moreover, we prove that if <em>X</em> is a nonempty weak^⁎ compact convex set having the weak^⁎ normal structure in a dual Banach space <span><math><mi>B</mi><msup><mrow></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> and <span><math><mi>J</mi></math></span> is the set of all surjective isometry mappings on <em>X</em> then <span><math><mi>J</mi></math></span> has a common fixed point in the Chebyshev center of <em>X</em>. In 2011, Aoyama and Kohsaka introduced the class of <em>α</em>-nonexpansive mappings in Banach spaces. In 2018, Amini et al. proved the weak fixed point property of an <em>α</em>-nonexpansive mapping in the presence of the normal structure. In this paper, we prove the weak^⁎ fixed point property of an <em>α</em>-nonexpansive mapping in the presence of the weak^⁎ normal structure. Further, we extend the fixed point result of Amini et al. for a commuting family of <em>α</em>-nonexpansive mappings.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 1","pages":"Article 129053"},"PeriodicalIF":1.2,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705434","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}

{"title":"A new approach to deriving Bäcklund transformations","authors":"A. Pickering","doi":"10.1016/j.jmaa.2024.129052","DOIUrl":"10.1016/j.jmaa.2024.129052","url":null,"abstract":"<div><div>We give a new, surprisingly simple approach to the derivation of Bäcklund transformations. Motivated by the use of integrating factors to solve linear ordinary differential equations, for the nonlinear case this new technique leads to differential relations between equations. Although our interest here is in Painlevé equations, our approach is applicable to nonlinear equations more widely. As a completely new result we obtain a matrix version of a classical mapping between solutions of special cases of the second Painlevé equation. This involves the derivation of a new matrix second Painlevé equation, for which we also present a Lax pair. In addition, we give a matrix version of the Schwarzian second Painlevé equation, again a completely new result. In this way we also discover a new definition of matrix Schwarzian derivative.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 1","pages":"Article 129052"},"PeriodicalIF":1.2,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The characterization of the image for the Weinstein heat transform","authors":"Nour Eddine Askour,&nbsp;Abdelilah El mourni,&nbsp;Imane El yazidi","doi":"10.1016/j.jmaa.2024.129050","DOIUrl":"10.1016/j.jmaa.2024.129050","url":null,"abstract":"<div><div>Based on reproducing kernel Hilbert space theory, this paper describes a result characterizing the image time-<em>t</em> heat transform associated with the Weinstein-Laplacian operator on half-space <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msubsup><mo>:</mo><mo>=</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>×</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mo>⁎</mo></mrow></msubsup></math></span>. The guiding principle behind characterization is this: the functions in the image of the heat transform should be those functions having an analytic continuation to the complex space <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span>, that are even in the last variable and that possess an appropriate <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-finite norm. Furthermore, we prove that the associated Bargmann transform with this heat transform is an isometric isomorphism (we referred to here as the Weinstein-Bargmann transform) for which we compute the inverse in an explicit form.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 2","pages":"Article 129050"},"PeriodicalIF":1.2,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697554","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}

{"title":"High-frequency asymptotic expansions for multiple scattering problems with Neumann boundary conditions","authors":"Yassine Boubendir ,&nbsp;Fatih Ecevit","doi":"10.1016/j.jmaa.2024.129047","DOIUrl":"10.1016/j.jmaa.2024.129047","url":null,"abstract":"<div><div>We consider the two-dimensional high-frequency plane wave scattering problem in the exterior of a finite collection of disjoint, compact, smooth (<span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>), strictly convex obstacles with Neumann boundary conditions. Using integral equation formulations, we determine the Hörmander classes and derive Melrose-Taylor type high-frequency asymptotic expansions of the total fields corresponding to multiple scattering iterations on the boundaries of the scattering obstacles. These asymptotic expansions are used to obtain sharp wavenumber dependent estimates on the derivatives of multiple scattering total fields. Numerical experiments supporting the validity of these expansions are presented.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 1","pages":"Article 129047"},"PeriodicalIF":1.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705433","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}

{"title":"On the behavior of solutions of some periodic differential equations","authors":"E. Ait Dads ,&nbsp;B. Es-sebbar ,&nbsp;L. Lhachimi","doi":"10.1016/j.jmaa.2024.129048","DOIUrl":"10.1016/j.jmaa.2024.129048","url":null,"abstract":"<div><div>This paper investigates the conditions that ensure the existence of unique periodic solutions for ordinary differential equations of the form <span><math><msup><mrow><mi>u</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>=</mo><mi>A</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>u</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span>, where both <span><math><mi>A</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> and <span><math><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> are <em>T</em>-periodic. Particular emphasis is placed on understanding the behavior of bounded solutions on <span><math><mi>R</mi></math></span>. Moreover, we examine cases where the equation's coefficients are nonnegative.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 1","pages":"Article 129048"},"PeriodicalIF":1.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705429","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}

{"title":"Rebricking frames and bases","authors":"Thomas Fink,&nbsp;Brigitte Forster,&nbsp;Florian Heinrich","doi":"10.1016/j.jmaa.2024.129051","DOIUrl":"10.1016/j.jmaa.2024.129051","url":null,"abstract":"<div><div>In 1949, Denis Gabor introduced the “complex signal” (nowadays called “analytic signal”) by combining a real function <em>f</em> with its Hilbert transform <em>Hf</em> to a complex function <span><math><mi>f</mi><mo>+</mo><mi>i</mi><mi>H</mi><mi>f</mi></math></span>. His aim was to extract phase information, an idea that has inspired techniques as the monogenic signal and the complex dual tree wavelet transform. In this manuscript, we consider two questions: When do two real-valued bases or frames <span><math><mo>{</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>:</mo><mi>n</mi><mo>∈</mo><mi>N</mi><mo>}</mo></math></span> and <span><math><mo>{</mo><msub><mrow><mi>g</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>:</mo><mi>n</mi><mo>∈</mo><mi>N</mi><mo>}</mo></math></span> form a complex basis or frame of the form <span><math><mo>{</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>+</mo><mi>i</mi><msub><mrow><mi>g</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>:</mo><mi>n</mi><mo>∈</mo><mi>N</mi><mo>}</mo></math></span>? And for which bounded linear operators <em>A</em> does <span><math><mo>{</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>+</mo><mi>i</mi><mi>A</mi><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>:</mo><mi>n</mi><mo>∈</mo><mi>N</mi><mo>}</mo></math></span> form a complex-valued orthonormal basis, Riesz basis or frame, when <span><math><mo>{</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>:</mo><mi>n</mi><mo>∈</mo><mi>N</mi><mo>}</mo></math></span> is a real-valued orthonormal basis, Riesz basis or frame? We call this approach <em>rebricking</em>. It is well-known that the analytic signals don't span the complex vector space <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>;</mo><mi>C</mi><mo>)</mo></math></span>, hence <em>H</em> is not a rebricking operator. We give a full characterization of rebricking operators for bases, in particular orthonormal and Riesz bases, Parseval frames, and frames in general. We also examine the special case of finite dimensional vector spaces and show that we can use any real, invertible matrix for rebricking if we allow for permutations in the imaginary part.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 2","pages":"Article 129051"},"PeriodicalIF":1.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142745808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Area functional and majorant series estimates in the class of bounded functions in the disk","authors":"R.S. Khasyanov","doi":"10.1016/j.jmaa.2024.129049","DOIUrl":"10.1016/j.jmaa.2024.129049","url":null,"abstract":"<div><div>In this article, the new inequalities for the weighted sums of coefficients in the class of bounded functions in the disk are obtained. We develop the methods of I.R. Kayumov and S. Ponnusamy, using E. Reich's theorem on the majorization of subordinate functions. The sharp estimates for the area of the image of the disk of radius <em>r</em> under the action of the function which is expanded into a lacunary series of standard form are obtained. Under significantly lower than in <span><span>[20]</span></span> restrictions on the initial coefficient, the estimates for the Bohr–Bombieri function of the Hadamard convolution operator are proved. Using the example of the differentiation operator, it is shown that in some cases the new method for calculating the lower bound for the Bohr radius of the Hadamard operator with a fixed initial coefficient is more effective than the known one.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129049"},"PeriodicalIF":1.2,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656133","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}