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Showing papers in "Mediterranean Journal of Mathematics in 2010"


Journal ArticleDOI
TL;DR: In this paper, the convergence properties of q-parametric Szasz-Mirakjan operators were studied and inequalities for the weighted approximation error were obtained in terms of weighted moduli of continuity.
Abstract: In the present paper, we introduce q-parametric Szasz-Mirakjan operators. We study convergence properties of these operators S n,q(f). We obtain inequalities for the weighted approximation error of q-Szasz-Mirakjan operators. Such inequalities are valid for functions of polynomial growth and are expressed in terms of weighted moduli of continuity. We also discuss Voronovskaja-type formula for q-Szasz-Mirakjan operators.

57 citations


Journal ArticleDOI
TL;DR: In this paper, the chaotic and hypercyclic behavior of the C ≥ 0-semigroups of operators generated by a perturbation of the Ornstein-Uhlenbeck operator with a multiple of the identity in $${L^2(\mathbb {R}^N}) is investigated, depending on the signs of real parts of the eigenvalues of the matrix appearing in the drift of the operator.
Abstract: The chaotic and hypercyclic behavior of the C 0-semigroups of operators generated by a perturbation of the Ornstein-Uhlenbeck operator with a multiple of the identity in $${L^2(\mathbb {R}^N)}$$ is investigated. Negative and positive results are presented, depending on the signs of the real parts of the eigenvalues of the matrix appearing in the drift of the operator.

35 citations


Journal ArticleDOI
TL;DR: In this paper, the order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for complex Bernstein-Durrmeyer polynomials attached to analytic functions on compact disks are obtained.
Abstract: In this paper, the order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for complex Bernstein-Durrmeyer polynomials attached to analytic functions on compact disks are obtained. In this way, we put in evidence the overconvergence phenomenon for Bernstein-Durrmeyer polynomials, namely the extensions of approximation properties (with quantitative estimates) from real intervals to compact disks in the complex plane.

29 citations


Journal ArticleDOI
TL;DR: In this article, general asymptotic and Voronovskaya theorems for simultaneous approximation were proved for the Durrmeyer and Bernstein operators, as well as for the Bernstein operator.
Abstract: In the present note we prove general asymptotic and Voronovskaya theorems for simultaneous approximation. These generalize the Voronovskaya type theorems obtained recently by Floater for the Bernstein operators, and previously by Heilmann and Muller for the Durrmeyer operators.

28 citations


Journal ArticleDOI
TL;DR: In this paper, a quantitative Voronovskaya formula for a class of Mellin convolution operators of type ============\/\/\/\/\/\/£££€££ ££ £ £ £££
Abstract: Here we give a quantitative Voronovskaya formula for a class of Mellin convolution operators of type $$({T_w}f)(s) = {\int_0^{+\infty}} {K_w}(zs^{-1})f(z)\frac{dz}{z}.$$ Moreover we furnish various applications to some classical operators.

22 citations


Journal ArticleDOI
TL;DR: In this paper, the Heisenberg-Pauli-Weyl inequality for the Fourier transform associated with the spherical mean operator is established and a generalization of this inequality is proved.
Abstract: The Heisenberg-Pauli-Weyl inequality is established for the Fourier transform associated with the spherical mean operator. Also, a generalization of this inequality is proved. Next, a local uncertainty principle is checked.

22 citations


Journal ArticleDOI
TL;DR: The main purpose of as mentioned in this paper is to study the Lp-boundedness of linear and bilinear multiplier operators for the Dunkl transform in the one-dimensional case.
Abstract: The main purpose of this article is to study the Lp-boundedness of linear and bilinear multiplier operators for the Dunkl transform in the one dimensional case.

22 citations


Journal ArticleDOI
TL;DR: In this article, the dependence of weighted eigenvalues of the one-dimensional p-Laplacian on indefinite integrable weights was studied and a simpler explanation to the corresponding spectrum problems was given with the help of several typical techniques in nonlinear analysis such as the Frechet derivative and weak* convergence.
Abstract: Motivated by extremal problems of weighted Dirichlet or Neumann eigenvalues, we will establish two fundamental results on the dependence of weighted eigenvalues of the one-dimensional p-Laplacian on indefinite integrable weights. One is the continuous differentiability of eigenvalues in weights in the Lebesgue spaces L γ with the usual norms. Another is the continuity of eigenvalues in weights with respect to the weak topologies in L γ spaces. Here 1 ≤ γ ≤ ∞. In doing so, we will give a simpler explanation to the corresponding spectrum problems, with the help of several typical techniques in nonlinear analysis such as the Frechet derivative and weak* convergence.

21 citations


Journal ArticleDOI
TL;DR: Good and s-good hyperlattices, homomorphism of hyper-attices and sreflexives are introduced in this article. But their structures are not studied. And they do not have a T0-space.
Abstract: In this paper by considering the notion of hyperlattice, we introduce good and s-good hyperlattices, homomorphism of hyperlattices and s-reflexives. We give some examples of them and we study their structures. We show that there exists a hyperlattice L such that \({x \vee x = \{x\}}\) for all \({x \in L}\) and there exist \({x, y \in L}\) which \({card(x \vee y) e 1}\). Also, we define a topology on the set of prime ideals of a distributive hyperlattice L and we will call it \({{{\mathcal S}(L)}}\), then we show that \({{{\mathcal S}(L)}}\) is a T0-space. At the end, we obtain that each complemented distributive hyperlattice is a T1-space.

19 citations


Journal ArticleDOI
Izu Vaisman1
TL;DR: In this article, a foliation of a Courant algebroid A is defined as a bracket-closed, isotropic subbundle B with an anchor image, such that A/B is locally equivalent with Lie algebroids over the slice manifolds of a foliated manifold.
Abstract: If A is a Lie algebroid over a foliated manifold \({(M, {\mathcal {F}})}\), a foliation of A is a Lie subalgebroid B with anchor image \({T{\mathcal {F}}}\) and such that A/B is locally equivalent with Lie algebroids over the slice manifolds of \({\mathcal F}\). We give several examples and, for foliated Lie algebroids, we discuss the following subjects: the dual Poisson structure and Vaintrob's supervector field, cohomology and deformations of the foliation, integration to a Lie groupoid. In the last section, we define a corresponding notion of a foliation of a Courant algebroid A as a bracket–closed, isotropic subbundle B with anchor image \({T{\mathcal {F}}}\) and such that \({B^{ \bot } /B}\) is locally equivalent with Courant algebroids over the slice manifolds of \({\mathcal F}\). Examples that motivate the definition are given.

14 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the summing sequence of polynomial hypergroups is equivalent to the growth condition (H) of the Haar weights h(n), which is also sufficient for the existence of means which satisfy a strong form of translation invariance.
Abstract: We investigate summing sequences in the context of polynomial hypergroups. It will be shown that the summing sequence \({(S_{n})_{n\in\mathbb{N}_{0}}}\), where Sn = {0, 1, . . . , n}, is equivalent to the growth condition (H) of the Haar weights h(n). This condition is also sufficient for the existence of means which satisfy a strong form of translation invariance. Furthermore we give exact representations of the unique translation invariant mean on the space of weakly almost periodic sequences for a large class of polynomial hypergroups.

Journal ArticleDOI
TL;DR: In this paper, the authors considered a linear system of Timoshenko type in a bounded interval and showed that damping occurs through a thermal effect by coupling the system with a heat equation suggested by Green and Naghdi.
Abstract: We consider a linear system of Timoshenko type in a bounded interval No dissipative mechanism is added in the system or at the edges of the beam The damping occurs through a thermal effect by coupling the system with a heat equation suggested by Green and Naghdi We prove exponential decay of solutions of the augmented system

Journal ArticleDOI
TL;DR: In this paper, it was shown that an absolute continuous embedding is not optimal and necessary and sufficient conditions for absolute continuity of these embeddings were given under additional hypotheses necessary.
Abstract: Compactness of embeddings between rearrangement invariant spaces is closely related to absolute continuity of these embeddings. We study absolutely continuous embeddings between rearrangement invariant spaces. In particular it is shown that an absolutely continuous embedding is never optimal. We give sufficient (and under additional hypotheses necessary) conditions for absolute continuity of these embeddings. We also provide quantitative estimates of absolutely continuous embeddings.

Journal ArticleDOI
TL;DR: In this article, the authors studied a general Korovkin-type approximation theory by using the notion of ideal convergence which includes many convergence methods, such as, the usual convergence, statistical convergence, A-statistical convergence, etc.
Abstract: In this paper, we study a general Korovkin-type approximation theory by using the notion of ideal convergence which includes many convergence methods, such as, the usual convergence, statistical convergence, A-statistical convergence, etc. We mainly compute the rate of ideal convergence of sequences of positive linear operators.

Journal ArticleDOI
TL;DR: In this article, a generalization of the square subgroup in the sense of [9] and its properties over a commutative domain are investigated. But the properties of square subgroups are not investigated.
Abstract: Let R be a commutative ring with identity, and M an R-module. We introduce square submodule, □M, of M as a generalization of the square subgroup in the sense of [9] and investigate its properties over a commutative domain.

Journal ArticleDOI
TL;DR: In this paper, the authors give sufficient conditions on the vector fields X>>\s for the existence of a Lie group structure, not necessarily nilpotent nor homogeneous, such that the system of vector fields is left invariant on the Lie group.
Abstract: If $${\mathcal{L} = {\sum_{j=1}^m} {X_j^2} + X_0}$$ is a Hormander partial differential operator in $${\mathbb{R}^N}$$ , we give sufficient conditions on the vector fields X j ’s for the existence of a Lie group structure $${\mathbb{G} = (\mathbb{R}^N, *)}$$ (and we exhibit its construction), not necessarily nilpotent nor homogeneous, such that $${\mathcal{L}}$$ is left invariant on $${\mathbb{G}}$$ . The main tool is a formula of Baker-Campbell-Dynkin-Hausdorff type for the ODE’s naturally related to the system of vector fields {X 0, . . . , X m }. We provide a direct proof of this formula in the ODE’s context (which seems to be missing in literature), without invoking any result of Lie group theory, nor the abstract algebraic machinery usually involved in formulas of Baker-Campbell-Dynkin-Hausdorff type. Examples of operators to which our results apply are also furnished.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated φ-Einstein contact Riemannian manifolds and applied it to Mathematics Subject Classification (2010) and found that φ = 0.
Abstract: φ-Einstein contact Riemannian manifolds are investigated. Mathematics Subject Classification (2010). Primary 58E20.

Journal ArticleDOI
TL;DR: In this article, the authors proved existence and comparison results for nonlinear parabolic equations which are modeled on the problem of finding a bounded open set in the Euclidean space.
Abstract: In this paper we prove existence and comparison results for nonlinear parabolic equations which are modeled on the problem $$\left\{\begin{array}{ll}{u_t - {\rm div}\,\left(\frac{1}{(1+|u|)^{\alpha}}|Du|^{p-2}Du\right) =f\quad\hskip 2pt \,\,{\rm in}\,\Omega\times(0,T),}\\ {u=0\qquad\qquad\qquad\qquad\quad\quad\qquad{\rm on}\,\partial\Omega\times(0,T),}\\ {u(x,0)=u_0(x)\quad\qquad\qquad\qquad\qquad{\rm in}\,\Omega,}\end{array}\right.$$ where T > 0, Ω is a bounded open set in $${\mathbb{R}^n, n \ge 2, 1 < p < n, \alpha \ge 0, f \in L^{\infty}(0, T;L^q(\Omega))}$$ , with q > n/p, and u 0 is a bounded function.

Journal ArticleDOI
TL;DR: In this article, a notion of restricted Walrasian expectations allocation is introduced and its relations with c-fairness is examined. But the notion of coalitional fairness requires that no coalition could benefit from achieving the net trade of some other disjoint coalition.
Abstract: We study relations among Walrasian expectations allocations, coalitional fair allocations and the private core of economies with uncertainty and asymmetric information. Our analysis covers finite exchange models, as well as models of mixed markets consisting of some large traders and an ocean of small traders. The adopted notion of coalitional fairness requires that: 1. Under a “c-fair” allocation, no coalition could benefit from achieving the net trade of some other disjoint coalition; 2. Coalition bargaining takes place without information sharing among agents. We introduce a notion of restricted Walrasian expectations allocation and examine its relations with c-fairness.

Journal ArticleDOI
TL;DR: In this paper, an algebraic characterization of generalized Sasakian-space-forms is presented, with particular attention to the k-nullity condition and pointwise constant curvature properties of l.c. C6-manifolds.
Abstract: An algebraic characterization of generalized Sasakian-space-forms is stated. Then, one studies the almost contact metric manifolds which are locally conformal to C6-manifolds, simply called l.c. C6-manifolds. In dimension 2n + 1 ≥ 5, any of these manifolds turns out to be locally conformal cosymplectic or globally conformal to a Sasakian manifold. Curvature properties of l.c. C6-manifolds are obtained, with particular attention to the k-nullity condition. This allows one to state a local classification theorem, in dimension 2n + 1 ≥ 5, under the hypothesis of constant sectional curvature. Moreover, one proves that an l.c. C6–manifold is a generalized Sasakian-space-form if and only if it satisfies the k-nullity condition and has pointwise constant \({\varphi}\)-sectional curvature. Finally, local classification theorems for the generalized Sasakian-space-forms in the considered class are obtained.

Journal ArticleDOI
TL;DR: In this article, second order regularity for the quasilinear elliptic equation ΔAu = f was established for the A-Laplace operator, where ΔA is the so-called A Laplace operator.
Abstract: In this paper we establish second order regularity for the quasilinear elliptic equation ΔAu = f, where ΔA is the so called A-Laplace operator

Journal ArticleDOI
TL;DR: In this paper, the special case of partial *-algebras of operators is examined, in order to find sufficient hints for the study of the abstract case, and the outcome consists in the selection of a class of topological GC*-alges that behave well from the spectral point of view and that allow, under certain conditions, a faithful realization as a partial O*algebra.
Abstract: We continue our study of topological partial *algebras focusing our attention to some basic spectral properties. The special case of partial *-algebras of operators is examined first, in order to find sufficient hints for the study of the abstract case. The outcome consists in the selection of a class of topological partial *-algebras (partial GC*-algebras) that behave well from the spectral point of view and that allow, under certain conditions, a faithful realization as a partial O*-algebra.

Journal ArticleDOI
TL;DR: In this article, the existence of extensions of a positive linear functional ω defined on a dense *-subalgebra of a topological *-algebra satisfying certain regularity conditions is examined.
Abstract: The existence of extensions of a positive linear functional ω defined on a dense *-subalgebra \({\mathfrak{A}_0}\) of a topological *-algebra \({\mathfrak{A}}\), satisfying certain regularity conditions, is examined. The main interest is focused on the case where ω is nonclosable and sufficient conditions for the existence of an absolutely convergent extension of ω are given.

Journal ArticleDOI
TL;DR: In this paper, the convergence of the Pizzetti series associated with the Dunkl Laplacian is studied and some properties of polyharmonic functions associated with this series are established.
Abstract: In this paper we are concerned with the Pizzetti series associated with the Dunkl Laplacian denoted Δ k . We study the convergence of this series and we give some applications. Next we establish some properties of polyharmonic functions associated with Δ k , especially, we establish Liouville type results.

Journal ArticleDOI
TL;DR: In this article, a description of all closed maximal ideals of continuous functions on a topological space is given with respect to the topology of the continuous functions and to the strict topology.
Abstract: Let X be a topological space, $${\mathfrak{S}}$$ a cover of X and $${C_{b}(X, \mathbb{K};\mathfrak{S})}$$ the algebra of all $${\mathbb{K}}$$ -valued continuous functions on X which are bounded on every $${S \in \mathfrak{S}}$$ . A description of all closed (in particular, all closed maximal) ideals of $${C_{b}(X,\mathbb{K};\mathfrak{S})}$$ is given with respect to the topology of $${\mathfrak{S}}$$ -convergence and to the $${\mathfrak{S}}$$ -strict topology.

Journal ArticleDOI
TL;DR: In this article, the Cartan-Dieudonne theorem is extended to nonisotropic hyperplanes with respect to bilinear morphisms, assuming that the coefficient sheaf of a Riemannian sheaf has nowhere-zero isotropic sections.
Abstract: Like the classical Cartan-Dieudonne theorem, the sheaf-theoretic version shows that \({\mathcal {A}}\)-isometries on a convenient \({\mathcal {A}}\)-module \({\mathcal {E}}\) of rank n can be decomposed in at most n orthogonal symmetries (reflections) with respect to non-isotropic hyperplanes. However, the coefficient sheaf of \({\mathbb {C}}\)-algebras \({\mathcal {A}}\) is assumed to be a PID \({\mathbb {C}}\)-algebra sheaf and, if \({(\mathcal {E},\phi)}\) is a pairing with \({\phi}\) a non-degenerate \({\mathcal {A}}\)-bilinear morphism, we assume that \({\mathcal {E}}\) has nowhere-zero (local) isotropic sections; but, for Riemannian sheaves of \({\mathcal {A}}\)-modules, this is not necessarily required.

Journal ArticleDOI
TL;DR: This article introduces two new asynchronous multisplitting methods for solving the system of weakly nonlinear equations Ax = G(x) in which A is an n × n real matrix and G( x) = (g1(x, g2(x), . . . , gn(x))T is a P-bounded mapping.
Abstract: In this article, we introduce two new asynchronous multisplitting methods for solving the system of weakly nonlinear equations Ax = G(x) in which A is an n × n real matrix and G(x) = (g1(x), g2(x), . . . , gn(x))T is a P-bounded mapping. First, by generalized accelerated overrelaxation (GAOR) technique, we introduce the asynchronous parallel multisplitting GAOR method (including the synchronous parallel multisplitting AOR method as a special case) for solving the system of weakly nonlinear equations. Second, asynchronous parallel multisplitting method based on symmetric successive overrelaxation (SSOR) multisplitting is introduced, which is called asynchronous parallel multisplitting SSOR method. Then under suitable conditions, we establish the convergence of the two introduced methods. The given results contain synchronous multisplitting iterations as a special case.

Journal ArticleDOI
TL;DR: In this article, a Dedekind complete vector lattice W containing positive linear forms is derived for a real, Archimedian ordered, vector space, whose positive cone V+ satisfies V = V+|V| + V|+ V||V+ |V| = V| − V| |V | = V
Abstract: Let V be a real, Archimedian ordered, vector space, whose positive cone V+ satisfies V = V+ – V+ To V we associate a Dedekind complete vector lattice W containing V (by abuse of notation) In the case when V has an order unit the determination of W is already known Let \({W_0 \subset W}\) be the vector lattice generated by V We study W0 in the case when the cone C of all positive linear forms on V separates the elements of V The determination of W0 involves the extreme rays of C We determine the cone of positive linear forms on W0 in terms of conical measures on C

Journal ArticleDOI
TL;DR: In this paper, the Ricci operator of a semi-symmetric Lorentzian three-manifolds admits a parallel degenerate line field, through a condition on the defining function f.
Abstract: We characterize semi-symmetric Lorentzian three-manifolds (M,gf) admitting a parallel degenerate line field, through a condition on the defining function f. The admissible Segre types of the Ricci operator of (M,gf) are also completely described, and semi-symmetric curvature homogeneous examples are presented in the possible different cases.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the isomorphisms of Orlicz-Kothe sequence spaces and quasidiagonal isomorphism of Cartesian products of ORL-power series spaces.
Abstract: In this manuscript, we investigate the isomorphisms of Orlicz-Kothe sequence spaces and quasidiagonal isomorphisms of Cartesian products of Orlicz-power series spaces.