# Journal of Inequalities and Applications

http://www.journalofinequalitiesandapplications.com/

## List of Papers (Total 3,386)

#### Boundedness of rough singular integral operators and commutators on Morrey-Herz spaces with variable exponents

By decomposing functions, we establish some boundedness results for some rough singular integrals on the homogeneous Morrey-Herz spaces M K ˙ q , p ( ⋅ ) α ( ⋅ ) , λ ( R n ) , where the two main indices are variable. The corresponding results as regards their commutators are also considered. MSC: 42B20, 42B25.

#### Index of a bivariate mean and applications

Exploring some results of (Raïssouli in J. Math. Inequal. 10(1):83-99, 2016 ) from another point of view, we introduce here some power-operations for (bivariate) means. As application, we construct some classes of means in one or two parameters including some standard means. We also define a law between means which allows us to obtain, among others, a simple relationship involving ...

#### Characterization of homogeneous symmetric monotone bivariate means

In this paper, we introduce a class of bivariate means generated by an integral of a continuous increasing function on ( 0 , + ∞ ) . This class of means widens the spectrum of possible means and leads to many easy and interesting mean-inequalities. We show that this class of means characterizes the large class of homogeneous symmetric monotone means. MSC: 26E60.

#### On the stability of finding approximate fixed points by simplicial methods

This paper reports some new results in relation to simplicial algorithms considering continuities of approximate fixed point sets. The upper semi-continuity of a set-valued mapping of approximate fixed points using vector-valued simplicial methods is proved, and thus one obtains the existence of finite essential connected components in approximate fixed point sets by vector-valued ...

#### On the complete convergence for weighted sums of a class of random variables

In this article, some new results as regards complete convergence for weighted sums ∑ i = 1 n a n i X i of random variables satisfying the Rosenthal type inequality are established under some mild conditions. These results extend the corresponding theorems of Deng et al. (Filomat 28(3):509-522, 2014 ) and Gan and Chen (Acta Math. Sci. 28(2):269-281, 2008 ). MSC: 60F15.

#### Boundedness and compactness of a new product-type operator from a general space to Bloch-type spaces

We characterize the boundedness and compactness of a product-type operator, which, among others, includes all the products of the single composition, multiplication, and differentiation operators, from a general space to Bloch-type spaces. We also give some upper and lower bounds for the norm of the operator. MSC: 47B38, 46E15.

#### Monotonicity and inequalities involving the incomplete gamma function

In the article, we deal with the monotonicity of the function x → [ ( x p + a ) 1 / p − x ] / I p ( x ) on the interval ( 0 , ∞ ) for p > 1 and a > 0 , and present the necessary and sufficient condition such that the double inequality [ ( x p + a ) 1 / p − x ] / a < I p ( x ) < [ ( x p + b ) 1 / p − x ] / b for all x > 0 and p > 1 , where I p ( x ) = e x p ∫ x ∞ e − t p d t is the ...

#### Monotonicity of a mean related to polygamma functions with an application

Let ψ n = ( − 1 ) n − 1 ψ ( n ) ( n = 0 , 1 , 2 , … ), where ψ ( n ) denotes the psi and polygamma functions. We prove that for n ≥ 0 and two different real numbers a and b, the function x ↦ ψ n − 1 ( ∫ a b ψ n ( x + t ) d t b − a ) − x is strictly increasing from ( − min ( a , b ) , ∞ ) onto ( min ( a , b ) , ( a + b ) / 2 ) , which generalizes a well-known result. As an ...

#### On the Hausdorff measure of noncompactness for the parameterized Prokhorov metric

We quantify the Prokhorov theorem by establishing an explicit formula for the Hausdorff measure of noncompactness (HMNC) for the parameterized Prokhorov metric on the set of Borel probability measures on a Polish space. Furthermore, we quantify the Arzelà-Ascoli theorem by obtaining upper and lower estimates for the HMNC for the uniform norm on the space of continuous maps of a ...

#### Ruin probabilities for a perturbed risk model with stochastic premiums and constant interest force

In this paper, we consider a perturbed compound Poisson risk model with stochastic premiums and constant interest force. We obtain the upper bound and Lundberg-Cramér approximation for the infinite-time ruin probability, and consider the asymptotic formula for the finite-time ruin probability when the claim size is heavy-tailed. We show that the model in our paper has similar ...

#### Shafer-type inequalities for inverse trigonometric functions and Gauss lemniscate functions

In this paper, we present Shafer-type inequalities for inverse trigonometric functions and Gauss lemniscate functions. MSC: 26D07.

#### A highly efficient spectral-Galerkin method based on tensor product for fourth-order Steklov equation with boundary eigenvalue

In this study, a highly efficient spectral-Galerkin method is posed for the fourth-order Steklov equation with boundary eigenvalue. By making use of the spectral theory of compact operators and the error formulas of projective operators, we first obtain the error estimates of approximative eigenvalues and eigenfunctions. Then we build a suitable set of basis functions included in H ...

#### Some new generalized Volterra-Fredholm type discrete fractional sum inequalities and their applications

In this paper, we present some new Volterra-Fredholm-type discrete fractional sum inequalities. These inequalities can be used as handy and powerful tools in the study of certain fractional sum-difference equations. Some applications are also presented to illustrate the usefulness of our results.

#### Bounds for triple gamma functions and their ratios

In this work, in addition to the bounds for triple gamma function, bounds for the ratios of triple gamma functions are obtained. Similar bounds for the ratios of the double gamma functions are also obtained. These results and their consequences are obtained using the known results of the gamma function. MSC: 33B15, 33A15, 26D07.

#### Bonnesen-style symmetric mixed inequalities

In this paper, we investigate the symmetric mixed isoperimetric deficit Δ 2 ( K 0 , K 1 ) of domains K 0 and K 1 in the Euclidean plane R 2 . Via the known kinematic formulae of Poincaré and Blaschke in integral geometry, we obtain some Bonnesen-style symmetric mixed inequalities. These new Bonnesen-style symmetric mixed inequalities are known as Bonnesen-style inequalities if one ...

#### An upper bound for solutions of the Lebesgue-Nagell equation x 2 + a 2 = y n

Let a be a positive integer with a > 1 , and let ( x , y , n ) be a positive integer solution of the equation x 2 + a 2 = y n , gcd ( x , y ) = 1 , n > 2 . Using Baker’s method, we prove that, for any positive number ϵ, if n is an odd integer with n > C ( ϵ ) , where C ( ϵ ) is an effectively computable constant depending only on ϵ, then n < ( 2 + ϵ ) ( log a ) / log y . Owing to ...

#### Topics on the spectral properties of degenerate non-self-adjoint differential operators

Let ( P u ) ( t ) = − d d t ( ω 2 ( t ) q ( t ) d u ( t ) d t ) be a degenerate non-self-adjoint operator defined on the space H ℓ = L 2 ( 0 , 1 ) ℓ with Dirichlet-type boundary conditions, where ω ( t ) ∈ C 1 ( 0 , 1 ) is a positive function with further assumptions that will be specified later, and q ( t ) ∈ C 2 ( [ 0 , 1 ] , End C ℓ ) is a matrix function. In this article, some ...

#### Difference of composition operators on weighted Bergman spaces over the half-plane

Recently, the bounded, compact and Hilbert-Schmidt difference of composition operators on the Bergman spaces over the half-plane are characterized in (Choe et al. in Trans. Am. Math. Soc., 2016 , in press). Motivated by this, we give a sufficient condition when two composition operators C φ and C ψ are in the same path component under the operator norm topology and show that there ...

#### 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 ...