In the paper, we establish a Lyapunov inequality and two Lyapunov-type inequalities for a higher-order fractional boundary value problem with a controllable nonlinear term. Two applications are discussed. One concerns an eigenvalue problem, the other a Mittag-Leffler function. MSC: 26A33, 26D10, 33E12, 34A08.

The main goal of the paper is to establish the boundedness of the fractional type Marcinkiewicz integral M β , ρ , q on non-homogeneous metric measure space which includes the upper doubling and the geometrically doubling conditions. Under the assumption that the kernel satisfies a certain Hörmander-type condition, the authors prove that M β , ρ , q is bounded from Lebesgue space L ...

In this paper, based on the modified Hermitian and skew-Hermitian splitting (MHSS) iteration method, the nonlinear MHSS-like iteration method is presented to solve a class of the weakly absolute value equations (AVE). By using a smoothing approximate function, the convergence properties of the nonlinear MHSS-like iteration method are presented. Numerical experiments are reported to ...

In high-dimensional models, the penalized method becomes an effective measure to select variables. We propose an adaptive bridge method and show its oracle property. The effectiveness of the proposed method is demonstrated by numerical results. MSC: 62F12, 62E15, 62J05.

Utilizing a new method to structure parallellotopes, a geometrical interpretation of the inverse matrix is given, which includes the generalized inverse of full column rank or a full row rank matrices. Further, some relational volume formulas of parallellotopes are established. MSC: 15A15, 52A20.

For singular nonsymmetric saddle-point problems, a shift-splitting preconditioner was studied in (Appl. Math. Comput. 269:947-955, 2015 ). To further show the efficiency of the shift-splitting preconditioner, we provide eigenvalue bounds for the nonzero eigenvalues of the shift-splitting preconditioned singular nonsymmetric saddle-point matrices. For real parts of the eigenvalues, ...

In this paper for interval systems we consider the problem of existence and evaluation of common diagonal solutions to the Lyapunov inequalities. For second order systems, we give necessary and sufficient conditions and exact solutions, that is, complete theoretical solutions. For third order systems, an algorithm for the evaluation of common solutions in the case of existence is ...

In this paper, a new S-type eigenvalue localization set for a tensor is derived by dividing N = { 1 , 2 , … , n } into disjoint subsets S and its complement. It is proved that this new set is sharper than those presented by Qi (J. Symb. Comput. 40:1302-1324, 2005 ), Li et al. (Numer. Linear Algebra Appl. 21:39-50, 2014 ) and Li et al. (Linear Algebra Appl. 481:36-53, 2015 ). As ...

We assume that X k = ∑ i = − ∞ + ∞ a i ξ i + k is a moving average process and { ξ i , − ∞ < i < + ∞ } is a doubly infinite sequence of identically distributed and dependent random variables with zero mean and finite variance and { a i , − ∞ < i < + ∞ } is an absolutely summable sequence of real numbers. Under suitable conditions of dependence, we get the precise rates in the law ...

Let T b → and T Π b be the commutators in the jth entry and iterated commutators of the multilinear Calderón-Zygmund operators, respectively. It was well known that the commutators of linear Calderón-Zygmund operators were not of weak type ( 1 , 1 ) and ( H 1 , L 1 ) , but they did satisfy certain endpoint L log L type estimates. In this paper, our aim is to give more natural sharp ...

By using the generalised Dirichlet integral inequality with continuous functions on the boundary of the upper half-space, we prove new types of solutions for the Neumann problem with fast-growing continuous data on the boundary. Given any harmonic function with its negative part satisfying similarly fast-growing conditions, we obtain weaker boundary integral condition.

The main purpose of this paper is to estimate the thickness of boundary layer for nonlinear evolution equations with damping and diffusion as the diffusion parameter β goes to zero. We prove that the thickness of layer is of the order O ( β γ ) with 0 < γ < 1 , thus improving the corresponding result in (Ruan and Zhu in Discrete Contin. Dyn. Syst. 32(1) 331-352, 2012 ) where 0 < γ ...

In the article, we discuss the monotonicity properties of the function x → ( 1 − e − a x p ) 1 / p / ∫ 0 x e − t p d t for a , p > 0 with p ≠ 1 on ( 0 , ∞ ) and prove that the double inequality Γ ( 1 + 1 / p ) ( 1 − e − a x p ) 1 / p < ∫ 0 x e − t p d t < Γ ( 1 + 1 / p ) ( 1 − e − b x p ) 1 / p holds for all x > 0 if and only if a ≤ min { 1 , Γ − p ( 1 + 1 / p ) } and b ≥ max { 1 , ...

In the present paper, we shall give a characterization for the Spanne and Adams type boundedness of the Riesz potential and its commutators on the generalized Orlicz-Morrey spaces, respectively. Also we give criteria for the weak versions of Spanne and Adams type boundedness of the Riesz potential on the generalized Orlicz-Morrey spaces. In all the cases the conditions for the ...

By applying some Schrödinger-type inequalities developed by Huang (Int. J. Math. 27(2):1650009, 2016 ), we are concerned with stabilization of discrete linear systems associated with the Schrödinger operator. Our first aim is to prove a state-dependent switching law associated with the Schrödinger operator, which is based on a convex combination. Next, we derive sufficient ...

The aim of this paper is to establish the decay estimate for the fractional wave equation semigroup on H-type groups given by e i t Δ α , 0 < α < 1 . Combining the dispersive estimate and a standard duality argument, we also derive the corresponding Strichartz inequalities. MSC: 22E25, 33C45, 35H20, 35B40.

Probabilistic frames have some properties which are similar to those of frames in Hilbert space. Some equalities and inequalities have been established for traditional frames. In this paper, we give some equalities and inequalities for probabilistic frames. Our results generalize and improve the remarkable results which have been obtained.

Bernstein inequality is an essential inequality for Besov spaces. Smoothness based approaches are widely used in establishing the inequality. Yet, despite numerous studies over the last two decades, there is still little research focusing on decay-based approaches. However, motivating authors to establish inequality poses challenges, many of which can be overcome by means of the ...

Anisotropy is a common attribute of Nature, which shows different characterizations in different directions of all or part of the physical or chemical properties of an object. The anisotropic property, in mathematics, can be expressed by a fairly general discrete group of dilations { A k : k ∈ Z } , where A is a real n × n matrix with all its eigenvalues λ satisfy | λ | > 1 . Let φ ...

We prove and discuss some new H p - L p type inequalities of weighted maximal operators of Vilenkin-Nörlund means with monotone coefficients. It is also proved that these inequalities are the best possible in a special sense. We also apply these results to prove strong summability for such Vilenkin-Nörlund means. As applications, both some well-known and new results are pointed ...

In this paper, we construct the geometric inequalities for the squared norm of the mean curvature and warping functions of warped product semi-slant submanifolds in Kenmotsu space forms. The equality cases are also discussed. MSC: 53C40, 58C35, 53C55, 53C42, 53C15, 53D15.

In this paper, we state and prove a new discrete q-fractional version of the Gronwall inequality. Based on this result, a particular version expressed by means of the q-Mittag-Leffler function is provided. To apply the proposed results, we prove the uniqueness and obtain an estimate for the solutions of nonlinear delay Caputo q-fractional difference system. We examine our results ...

This paper deals with the existence and multiplicity of symmetric solutions for a weighted semilinear elliptic system with multiple critical Hardy-Sobolev exponents and singular potentials in R N . Applying the symmetric criticality principle and Caffarelli-Kohn-Nirenberg inequality, we establish several existence and multiplicity results of G-symmetric solutions under certain ...

The complete characterization of the weighted L p − L r inequalities of supremum operators on the cones of monotone functions for all 0 < p , r ≤ ∞ is given. MSC: 26D15, 47G10.

This paper shows some continuities of mappings between the space of mixed variational inequality problems and the graph space of their solution mappings. The space of mixed variational inequality problems is homeomorphic to the graph of a continuous mapping. These generalize the results in the corresponding references. MSC: 49J53, 58E35, 47H04.