# Journal of Inequalities and Applications

http://www.journalofinequalitiesandapplications.com/

## List of Papers (Total 3,388)

#### Existence and uniqueness of solutions for a class of integral equations by common fixed point theorems in IFMT-spaces

In this paper, our aim is to address the existence and uniqueness of solutions for a class of integral equations in IFMT-space. Therefore, we introduce the concept of IFMT-spaces and prove a common fixed point theorem in a complete IFMT-space; next we study an application. MSC: 54E40, 54E35, 54H25.

#### Optimal Hyers-Ulam’s constant for the linear differential equations

In this paper, we will obtain the optimal Hyers-Ulam’s constant for the first-order linear differential equations p ( t ) y ′ ( t ) − q ( t ) y ( t ) − r ( t ) = 0 . MSC: 34A40, 34D10, 34A30, 39B82.

#### Convergence results of a matrix splitting algorithm for solving weakly nonlinear complementarity problems

In this paper, we consider a class of weakly nonlinear complementarity problems (WNCP) with large sparse matrix. We present an accelerated modulus-based matrix splitting algorithm by reformulating the WNCP as implicit fixed point equations based on two splittings of the system matrixes. We show that, if the system matrix is a P-matrix, then under some mild conditions the sequence ...

#### Fractional Brownian sheet and martingale difference random fields

In this paper, we prove a functional central limit theorem for the multidimensional parameter fractional Brownian sheet using martingale difference random fields. The proof is based on the invariance principle for the Brownian sheet due Poghosyan and Roelly (Stat. Probab. Lett. 38:235-245, 1998 ). MSC: 60B10, 60G15.

#### Monotonicity and absolute monotonicity for the two-parameter hyperbolic and trigonometric functions with applications

In this paper, we present the monotonicity and absolute monotonicity properties for the two-parameter hyperbolic and trigonometric functions. As applications, we find several complete monotonicity properties for the functions involving the gamma function and provide the bounds for the error function. MSC: 33B10, 33B15, 33B20, 26A48, 26D07.

#### Boundedness of fractional integrals on weighted Herz spaces with variable exponent

Our aim is to prove the boundedness of fractional integral operators on weighted Herz spaces with variable exponent. Our method is based on the theory on Banach function spaces and the Muckenhoupt theory with variable exponent. MSC: 42B35.

#### Solving total-variation image super-resolution problems via proximal symmetric alternating direction methods

The single image super-resolution (SISR) problem represents a class of efficient models appealing in many computer vision applications. In this paper, we focus on designing a proximal symmetric alternating direction method of multipliers (SADMM) for the SISR problem. By taking full exploitation of the special structure, the method enjoys the advantage of being easily implementable ...

#### Improvements of the bounds for Ramanujan constant function

In the article, we establish several inequalities for the Ramanujan constant function R ( x ) = − 2 γ − ψ ( x ) − ψ ( 1 − x ) on the interval ( 0 , 1 / 2 ] , where ψ ( x ) is the classical psi function and γ = 0.577215 ⋯ is the Euler-Mascheroni constant. MSC: 33B15, 26D07.

#### Projected Tikhonov regularization method for Fredholm integral equations of the first kind

In this paper, we consider a variant of projected Tikhonov regularization method for solving Fredholm integral equations of the first kind. We give a theoretical analysis of this method in the Hilbert space L 2 ( a , b ) setting and establish some convergence rates under certain regularity assumption on the exact solution and the kernel k ( ⋅ , ⋅ ) . Some numerical results are also ...

#### The weighted reverse Poincaré-type estimates for the difference of two convex vectors

In this paper we develop Caccioppoli-type estimates for arbitrary convex vectors and the vectors having both convex and concave arguments. To do this, we first develop these estimates for smooth convex vectors and then, through mollification, extend the results for arbitrary convex vectors. These types of estimates are valuable in the problems of financial mathematics for the ...

#### Compact matrix operators on a new sequence space related to ℓ p spaces

In this paper, we derive some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the sequence space ℓ p ( r , s , t ; B ( m ) ) which is related to ℓ p spaces. By applying the Hausdorff measure of noncompactness, we obtain the necessary and sufficient conditions for such operators to be compact. Further, we ...

#### Weak Poincaré inequalities and hitting times for jump processes

In this paper, we get a criteria of weak Poincaré inequality by some integrability of hitting times for jump processes. In fact, integrability of hitting times on a subset F of state space E implies that the taboo process restricted on E ∖ F is decay, from which we get a weak Poincaré inequality with absorbing (Dirichlet) boundary. Using it and a local Poincaré inequality, we ...

#### A Crank-Nicolson finite volume element method for two-dimensional Sobolev equations

In this paper, we provide a new type of study approach for the two-dimensional (2D) Sobolev equations. We first establish a semi-discrete Crank-Nicolson (CN) formulation with second-order accuracy about time for the 2D Sobolev equations. Then we directly establish a fully discrete CN finite volume element (CNFVE) formulation from the semi-discrete CN formulation about time and ...

#### Eigenvalue inequalities of elliptic operators in weighted divergence form on smooth metric measure spaces

In this paper, we study the eigenvalue problem of elliptic operators in weighted divergence form on smooth metric measure spaces. First of all, we give a general inequality for eigenvalues of the eigenvalue problem of elliptic operators in weighted divergence form on compact smooth metric measure space with boundary (possibly empty). Then applying this general inequality, we get ...

#### Lyapunov-type inequalities for a fractional p-Laplacian equation

In this paper, we present new Lyapunov-type inequalities for a fractional boundary value problem that models a turbulent flow in a porous medium. The obtained inequalities are used to obtain a lower bound for the eigenvalues of corresponding equations. MSC: 34A08, 15A42, 26D15, 76F70.

#### On ( p , q ) -analogue of two parametric Stancu-Beta operators

Our purpose is to introduce a two-parametric ( p , q ) -analogue of the Stancu-Beta operators. We study approximating properties of these operators using the Korovkin approximation theorem and also study a direct theorem. We also obtain the Voronovskaya-type estimate for these operators. Furthermore, we study the weighted approximation results and pointwise estimates for these ...

#### Generalized Wilker-type inequalities with two parameters

In the article, we present certain p , q ∈ R such that the Wilker-type inequalities 2 q p + 2 q ( sin x x ) p + p p + 2 q ( tan x x ) q > ( < ) 1 and ( π 2 ) p ( sin x x ) p + [ 1 − ( π 2 ) p ] ( tan x x ) q > ( < ) 1 hold for all x ∈ ( 0 , π / 2 ) . MSC: 26D05, 33B10.

#### Dilation-and-modulation systems on the half real line

Translation, dilation, and modulation are fundamental operations in wavelet analysis. Affine frames based on translation-and-dilation operation and Gabor frames based on translation-and-modulation operation have been extensively studied and seen great achievements. But dilation-and-modulation frames have not. This paper addresses a class of dilation-and-modulation systems in L 2 ( ...

#### Smoothing of the lower-order exact penalty function for inequality constrained optimization

In this paper, we propose a method to smooth the general lower-order exact penalty function for inequality constrained optimization. We prove that an approximation global solution of the original problem can be obtained by searching a global solution of the smoothed penalty problem. We develop an algorithm based on the smoothed penalty function. It is shown that the algorithm is ...

#### A rank formula for the self-commutators of rational Toeplitz tuples

In this paper we derive a rank formula for the self-commutators of tuples of Toeplitz operators with matrix-valued rational symbols. MSC: 47B20, 47B35, 47A13, 30H10, 47A57.

#### Some Brunn-Minkowski type inequalities for L p radial Blaschke-Minkowski homomorphisms

Schuster introduced radial Blaschke-Minkowski homomorphisms. Recently, they were generalized to L p radial Blaschke-Minkowski homomorphisms by Wang et al. In this paper, we first establish Brunn-Minkowski type inequalities for some L q radial sums of L p radial Blaschke-Minkowski homomorphisms. Further, we consider monotonic inequalities for L p radial Blaschke-Minkowski ...

#### Equalities and inequalities for ranks of products of generalized inverses of two matrices and their applications

A complex matrix X is called an { i , … , j } -inverse of the complex matrix A, denoted by A ( i , … , j ) , if it satisfies the ith, …, jth equations of the four matrix equations (i) A X A = A , (ii) X A X = X , (iii) ( A X ) ∗ = A X , (iv) ( X A ) ∗ = X A . The eight frequently used generalized inverses of A are A † , A ( 1 , 3 , 4 ) , A ( 1 , 2 , 4 ) , A ( 1 , 2 , 3 ) , A ( 1 , ...

#### A kind of boundary value problem for inhomogeneous partial differential system

In this article, we first define a kind of generalized singular integral operator and discuss its properties. Then we propose a kind of boundary value problem for an inhomogeneous partial differential system in R 4 . Finally, the integral representation of the solution to a boundary value problem for the inhomogeneous partial differential system is obtained using the above singular ...

#### Maximum norm analysis of a nonmatching grids method for a class of variational inequalities with nonlinear source terms

In this paper, we study a nonmatching grid finite element approximation of a class of elliptic variational inequalities with nonlinear source terms in the context of the Schwarz alternating domain decomposition. We show that the approximation converges optimally in the maximum norm, on each subdomain, making use of a Lipschitz continuous dependence with respect to both the boundary ...

#### An invariant subspace problem for multilinear operators on Banach spaces and algebras

This paper is concerned with the study of invariant subspace problems for nonlinear operators on Banach spaces/algebras. Our study reveals that one faces unprecedented challenges such as lack of vector space structure and unbounded spectral sets when tackling invariant subspace problems for nonlinear operators via spectral information. To bypass some of these challenges, we ...