Mediterranean Journal of Mathematics最新文献

We establish two direct estimates by K-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.

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 J-invariant, (J^{*})-invariant and anti-invariant generalized Kähler-like statistical submersions.

In this paper, two problems related to the following class of elliptic Kirchhoff–Boussinesq-type models are analyzed in the subcritical ((beta =0)) and critical ((beta =1)) cases:

where (tau >0), (2< p< 2^{*}= frac{2N}{N-2}) for ( Nge 3) and (2_{**}= infty ) for (N=3), (N=4), (2_{**}= frac{2N}{N-4}) for (Nge 5). 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.

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.

We consider the magnetic Schrödinger operator (H=(i nabla +A)^2- V) with a non-negative potential V supported over a strip which is a local deformation of a straight one, and the magnetic field (B:=textrm{rot}(A)) 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 H to be empty.

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.

In the present paper, we introduce a new family of sampling operators, so-called “modified sampling operators”, by taking a function (rho ) 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 (rho ) 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.

In this paper, we prove that a proper subdomain (Omega ) of (mathbb {R}^n) equipped with the metric (i_{Omega }), recently introduced by Nikolov and Andreev, is Gromov hyperbolic. We also show that there is a natural quasisymmetric correspondence between the Euclidean boundary of (Omega ) (with respect to (overline{mathbb {R}^n})) and the Gromov boundary of ((Omega ,i_Omega )).

We investigate the (D_{omega })-classical orthogonal polynomials, where (D_{omega }) is the weighted difference operator. So, we address the problem of finding the sequence of orthogonal polynomials such that their (D_{omega })-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 (omega =0), we rediscover the classical orthogonal polynomials of Hermite, Laguerre, Bessel and Jacobi. For (omega =1), we encounter the families of discrete classical orthogonal polynomials as particular cases.

We focus on investigating the differential geometric properties of cuspidal edge in the three-sphere from a viewpoint of duality. Using Legendrian duality, we study a special kind of flat surface along cuspidal edge in three-dimensional sphere space. This kind of surface is dual to the singular set of the cuspidal edge surface. Thus, we call it the flat (Delta )-dual surface. Flatness of a surface can be defined by the degeneracy of the dual surface. It is similar to the case for the Gauss map of a flat surface in Euclidean space. Moreover, classifications of singularities of the flat (Delta )-dual surface are shown. We also investigate the dual relationships of singularities between flat (Delta )-dual surface and flat approximations of the original cuspidal edge surface. At last, we consider a global geometry of the singular set of a cuspidal edge surface using the flat (Delta )-dual surface.