Journal of Inequalities and Applications

http://www.journalofinequalitiesandapplications.com/

List of Papers (Total 3,386)

Iterative methods of strong convergence theorems for the split feasibility problem in Hilbert spaces

In this paper, we propose several new iterative algorithms to solve the split feasibility problem in the Hilbert spaces. By virtue of new analytical techniques, we prove that the iterative sequence generated by these iterative procedures converges to the solution of the split feasibility problem which is the best close to a given point. In particular, the minimum-norm solution can ...

Some trace inequalities for matrix means

In this short note, we present some trace inequalities for matrix means. Our results are generalizations of the ones shown by Bhatia, Lim, and Yamazaki. MSC: 47A63.

An effective finite element Newton method for 2D p-Laplace equation with particular initial iterative function

In this article, a functional minimum problem equivalent to the p-Laplace equation is introduced, a finite element-Newton iteration formula is established, and a well-posed condition of iterative functions satisfied is provided. According to the well-posed condition, an effective initial iterative function is presented. Using the effective particular initial function and Newton ...

A selected method for the optimal parameters of the AOR iteration

In this paper, we present an optimization technique to find the optimal parameters of the AOR iteration, which just needs to minimize the 2-norm of the residual vector and avoids solving the spectral radius of the iteration matrix of the SOR method. Meanwhile, numerical results are provided to indicate that the new method is more robust than the AOR method for larger intervals of ...

Convergence of a space-time continuous Galerkin method for the wave equation

This paper gives a new theoretical analysis of the space-time continuous Galerkin (STCG) method for the wave equation. We prove the existence and uniqueness of the numerical solutions and get optimal orders of convergence to numerical solutions regarding space that do not need any compatibility conditions on the space and time mesh size. Finally, we employ a numerical example to ...

The ratio log-concavity of the Cohen numbers

Let U n denote the nth Cohen number. Some combinatorial properties for U n have been discovered. In this paper, we prove the ratio log-concavity of U n by establishing the lower and upper bounds for U n U n − 1 . MSC: 05A20, 11B83.

Lagrange-type duality in DC programming problems with equivalent DC inequalities

In this paper, we provide Lagrange-type duality theorems for mathematical programming problems with DC objective and constraint functions. The class of problems to which Lagrange-type duality theorems can be applied is broader than the class in the previous research. The main idea is to consider equivalent inequality systems given by the maximization of the original functions. In ...

Multilinear fractional integral operators on non-homogeneous metric measure spaces

In this paper, the boundedness in Lebesgue spaces for multilinear fractional integral operators and commutators generated by multilinear fractional integrals with an RBMO ( μ ) function on non-homogeneous metric measure spaces is obtained. MSC: 42B25, 47B47.

Sub-super-stabilizability of certain bivariate means via mean-convexity

In this paper, we first show that the first Seiffert mean P is concave whereas the second Seiffert mean T and the Neuman-Sándor mean NS are convex. As applications, we establish the sub-stabilizability/super-stabilizability of certain bivariate means. Open problems are derived as well. MSC: 26E60.

A note on Cauchy-Lipschitz-Picard theorem

In this note, we try to generalize the classical Cauchy-Lipschitz-Picard theorem on the global existence and uniqueness for the Cauchy initial value problem of the ordinary differential equation with global Lipschitz condition, and we try to weaken the global Lipschitz condition. We can also get the global existence and uniqueness. MSC: 34A34, 34C25, 34C37.

Proof of a conjecture of Z-W Sun on ratio monotonicity

In this paper, we study the log-behavior of a new sequence { S n } n = 0 ∞ , which was defined by Z-W Sun. We find that the sequence is log-convex by using the interlacing method. Additionally, we consider ratio log-behavior of { S n } n = 0 ∞ and find the sequences { S n + 1 / S n } n = 0 ∞ and { S n n } n = 1 ∞ are log-concave. Our results give an affirmative answer to a ...

Norm inequalities for operators related to the Cauchy-Schwarz and Heinz inequalities

We present some refinements of the Cauchy-Schwarz and Heinz inequalities for operators by utilizing a refinement of the Hermite-Hadamard inequality. MSC: 15A45, 15A60.

Character sums over generalized Lehmer numbers

Let q > 2 be an integer, n ⩾ 2 be a fixed integer with ( n , q ) = 1 , ψ be a non-principal Dirichlet character modq. An upper bound estimate for character sums of the form ∑ a ∈ C ( 1 , q ) ψ ( a ) is given, where C ( 1 , q ) = { a ∣ 1 ⩽ a ⩽ q − 1 , a a ‾ ≡ 1 ( mod q ) , n ∤ ( a + a ‾ ) } . MSC: 11L05, 11L40, 11N37.

Some remarks on Cîrtoaje’s conjecture

In this paper, we give new conditions under which the Cîrtoaje’s conjecture is also valid. We also show that a certain generalization of the Cîrtoaje’s inequality fulfils an interesting property. MSC: 26D10, 26D15.

Two new lower bounds for the minimum eigenvalue of M-tensors

Two new lower bounds for the minimum eigenvalue of an irreducible M-tensor are given. It is proved that the new lower bounds improve the corresponding bounds obtained by He and Huang (J. Inequal. Appl. 2014:114, 2014 ). Numerical examples are given to verify the theoretical results. MSC: 15A18, 15A69, 65F10, 65F15.

Hausdorff measure of noncompactness of matrix operators on some new difference sequence spaces

The new sequence spaces X ( r , s , t ; Δ ) for X ∈ { l ∞ , c , c 0 } have been defined by using generalized means and difference operator. In this work, we establish identities or estimates for the operator norms and the Hausdorff measure of noncompactness of certain matrix operators on some new difference sequence spaces X ( r , s , t ; Δ ) where X ∈ { l ∞ , c , c 0 , l p } ( 1 ≤ ...

Optimality conditions for strict minimizers of higher-order in semi-infinite multi-objective optimization

This paper is devoted to the study of optimality conditions for strict minimizers of higher-order for a non-smooth semi-infinite multi-objective optimization problem. We propose a generalized Guignard constraint qualification and a generalized Abadie constraint qualification for this problem under which necessary optimality conditions are proved. Under the assumptions of ...

Some determinantal inequalities for Hadamard and Fan products of matrices

In this note, we generalize some determinantal inequalities which are due to Lynn (Proc. Camb. Philos. 60:425-431, 1964 ), Chen (Linear Algebra Appl. 368:99-106, 2003 ) and Ando (Linear Multilinear Algebra 8:291-316, 1980 ). MSC: 47A63, 47A30.

A generalized Lyapunov inequality for a higher-order fractional boundary value problem

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.

Fractional type Marcinkiewicz integrals over non-homogeneous metric measure spaces

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 ...

On the modified Hermitian and skew-Hermitian splitting iteration methods for a class of weakly absolute value equations

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 ...

Adaptive bridge estimation for high-dimensional regression models

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.

A geometrical interpretation of the inverse matrix

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.

Eigenvalue bounds of the shift-splitting preconditioned singular nonsymmetric saddle-point matrices

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, ...

Common diagonal solutions to the Lyapunov inequalities for interval systems

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 ...