{"title":"A Generalization of the Isosceles Constant in Banach Spaces","authors":"Marco Baronti, Valentina Bertella","doi":"10.1007/s00009-024-02654-9","DOIUrl":"https://doi.org/10.1007/s00009-024-02654-9","url":null,"abstract":"<p>N. Gastinel and J.L. Joly defined the rectangular constant <span>(mu )</span> in Banach spaces using the notion of orthogonality according to Birkhoff and its generalization <span>(mu _p)</span>, with <span>(pge 1)</span>. Recently, M. Baronti, E. Casini, and P.L. Papini defined a new constant, the isosceles constant <i>H</i>, in Banach spaces in a very similar way to the rectangular constant, but in this case using the isosceles orthogonality defined by James. In this paper, first of all, we generalize such constant, by defining a new constant <span>(H_p)</span> that generalizes the isosceles constant <i>H</i> as well <span>(mu _p)</span> generalizes <span>(mu )</span>. After that, we explain its properties, and we give a characterization of Hilbert spaces in terms of it. Moreover a partial characterization of uniformly non-square spaces is given. We conclude by a conjecture about the characterization of uniformly non-square spaces.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886406","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":"Direct Estimates of the Rate of Approximation by the Kantorovich Operator in Variable Exponent Lebesgue Spaces","authors":"Borislav R. Draganov, Ivan Gadjev","doi":"10.1007/s00009-024-02650-z","DOIUrl":"https://doi.org/10.1007/s00009-024-02650-z","url":null,"abstract":"<p>We establish two direct estimates by <i>K</i>-functionals of the rate of approximation by the Kantorovich operators in variable exponent Lebesgue spaces. They extend known results in the non-variable exponent Lebesgue spaces. The approach applied heavily relies on the boundedness of the Hardy–Littlewood maximal operator.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"32 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886103","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":"Statistical Submersions with Parallel Almost Complex Structures","authors":"Kazuhiko Takano, Sema Kazan","doi":"10.1007/s00009-024-02621-4","DOIUrl":"https://doi.org/10.1007/s00009-024-02621-4","url":null,"abstract":"<p>The aim of the present paper is to study statistical submersions with parallel almost complex structures. First, we define the notion of the generalized Kähler-like statistical submersion and give examples of the Kähler-like statistical submersions. In addition, we investigate total space and fibers under certain conditions. After, we introduce some results on <i>J</i>-invariant, <span>(J^{*})</span>-invariant and anti-invariant generalized Kähler-like statistical submersions.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"38 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140826562","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":"Existence and Multiplicity of Solutions for a Class of Kirchhoff–Boussinesq-Type Problems with Logarithmic Growth","authors":"Romulo D. Carlos, Lamine Mbarki, Shuang Yang","doi":"10.1007/s00009-024-02649-6","DOIUrl":"https://doi.org/10.1007/s00009-024-02649-6","url":null,"abstract":"<p>In this paper, two problems related to the following class of elliptic Kirchhoff–Boussinesq-type models are analyzed in the subcritical (<span>(beta =0)</span>) and critical (<span>(beta =1)</span>) cases: </p><span>$$begin{aligned} Delta ^{2} u !- !Delta _p u !=! tau |u|^{q-2} u{ln |u|}!+!beta |u|^{2_{**}-2}u text{ in } Omega text{ and } {Delta u=u=0} text{ on } partial Omega , end{aligned}$$</span><p>where <span>(tau >0)</span>, <span>(2< p< 2^{*}= frac{2N}{N-2})</span> for <span>( Nge 3)</span> and <span>(2_{**}= infty )</span> for <span>(N=3)</span>, <span>(N=4)</span>, <span>(2_{**}= frac{2N}{N-4})</span> for <span>(Nge 5)</span>. The first one is concerned with the existence of a nontrivial ground-state solution via variational methods. As for the second problem, we prove the multiplicity of such a solution using the Mountain Pass Theorem.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"161 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140841824","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}
Juan Ferrera, Mohamad R. Pouryayevali, Hajar Radmanesh
{"title":"Local Minimality of Weak Geodesics on Prox-Regular Subsets of Riemannian Manifolds","authors":"Juan Ferrera, Mohamad R. Pouryayevali, Hajar Radmanesh","doi":"10.1007/s00009-024-02648-7","DOIUrl":"https://doi.org/10.1007/s00009-024-02648-7","url":null,"abstract":"<p>In this paper, we prove that every locally minimizing curve with constant speed in a prox-regular subset of a Riemannian manifold is a weak geodesic. Moreover, it is shown that under certain assumptions, every weak geodesic is locally minimizing. Furthermore, a notion of closed weak geodesics on prox-regular sets is introduced and a characterization of these curves as nonsmooth critical points of the energy functional is presented.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"32 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140840398","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}
Juan Bory-Reyes, Diana Barseghyan, Baruch Schneider
{"title":"Magnetic Schrödinger Operator with the Potential Supported in a Curved Two-Dimensional Strip","authors":"Juan Bory-Reyes, Diana Barseghyan, Baruch Schneider","doi":"10.1007/s00009-024-02651-y","DOIUrl":"https://doi.org/10.1007/s00009-024-02651-y","url":null,"abstract":"<p>We consider the magnetic Schrödinger operator <span>(H=(i nabla +A)^2- V)</span> with a non-negative potential <i>V</i> supported over a strip which is a local deformation of a straight one, and the magnetic field <span>(B:=textrm{rot}(A))</span> is assumed to be non-zero and local. We show that the magnetic field does not change the essential spectrum of this system, and investigate a sufficient condition for the discrete spectrum of <i>H</i> to be empty.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"157 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140840387","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":"The Duality Theory of Fractional Calculus and a New Fractional Calculus of Variations Involving Left Operators Only","authors":"Delfim F. M. Torres","doi":"10.1007/s00009-024-02652-x","DOIUrl":"https://doi.org/10.1007/s00009-024-02652-x","url":null,"abstract":"<p>Through duality, it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or right operators. The emergence of these novel fractional integration by parts formulas inspires the introduction of a new calculus of variations, where only one type of fractional derivative (left or right) is present. This applies to both the problem formulation and the corresponding necessary optimality conditions. As a practical application, we present a new Lagrangian that relies solely on left-hand side fractional derivatives. The fractional variational principle derived from this Lagrangian leads us to the equation of motion for a dissipative/damped system.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"88 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140826701","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":"Approximation by Modified Generalized Sampling Series","authors":"Metin Turgay, Tuncer Acar","doi":"10.1007/s00009-024-02653-w","DOIUrl":"https://doi.org/10.1007/s00009-024-02653-w","url":null,"abstract":"<p>In the present paper, we introduce a new family of sampling operators, so-called “modified sampling operators”, by taking a function <span>(rho )</span> that satisfies the suitable conditions, and we study pointwise and uniform convergence of the family of newly introduced operators. We give the rate of convergence of the family of operators via classical modulus of continuity. We also obtain an asymptotic formula in the sense of Voronovskaja. Moreover, we investigate the approximation properties of modified sampling operators in weighted spaces of continuous functions characterized by <span>(rho )</span> function. Finally, we present examples of some kernels that satisfy the appropriate assumptions. At the end, we present some graphical and numerical representations by comparing the modified sampling operators and the classical sampling operators.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"21 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140840462","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}
Qianghua Luo, Antti Rasila, Ye Wang, Qingshan Zhou
{"title":"The Nikolov–Andreev Metric and Gromov Hyperbolicity","authors":"Qianghua Luo, Antti Rasila, Ye Wang, Qingshan Zhou","doi":"10.1007/s00009-024-02655-8","DOIUrl":"https://doi.org/10.1007/s00009-024-02655-8","url":null,"abstract":"<p>In this paper, we prove that a proper subdomain <span>(Omega )</span> of <span>(mathbb {R}^n)</span> equipped with the metric <span>(i_{Omega })</span>, recently introduced by Nikolov and Andreev, is Gromov hyperbolic. We also show that there is a natural quasisymmetric correspondence between the Euclidean boundary of <span>(Omega )</span> (with respect to <span>(overline{mathbb {R}^n})</span>) and the Gromov boundary of <span>((Omega ,i_Omega ))</span>.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"4 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140809522","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 $$D_{omega }$$ -Classical Orthogonal Polynomials","authors":"Khalfa Douak","doi":"10.1007/s00009-024-02638-9","DOIUrl":"https://doi.org/10.1007/s00009-024-02638-9","url":null,"abstract":"<p>We investigate the <span>(D_{omega })</span>-classical orthogonal polynomials, where <span>(D_{omega })</span> is the weighted difference operator. So, we address the problem of finding the sequence of orthogonal polynomials such that their <span>(D_{omega })</span>-derivatives is also orthogonal polynomials. To solve this problem we adopt a different approach to those employed in this topic. We first begin by determining the coefficients involved in their recurrence relations, and then providing an exhaustive list of all solutions. When <span>(omega =0)</span>, we rediscover the classical orthogonal polynomials of Hermite, Laguerre, Bessel and Jacobi. For <span>(omega =1)</span>, we encounter the families of discrete classical orthogonal polynomials as particular cases.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"12 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140809543","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}