Journal of Inequalities and Applications

List of Papers (Total 3,386)

Nonlinear problem with subcritical exponent in Sobolev space

Using Brouwer’s fixed point theorem, we prove the existence of solutions for some nonlinear problem with subcritical Sobolev exponent in S + 4 . MSC: 46E35, 47H10, 35J60.

The binomial sequence spaces which include the spaces ℓ p and ℓ ∞ and geometric properties

In this work, we introduce the binomial sequence spaces b p r , s and b ∞ r , s which include the spaces ℓ p and ℓ ∞ , in turn. Moreover, we show that the spaces b p r , s and b ∞ r , s are BK-spaces and prove that these spaces are linearly isomorphic to the spaces ℓ p and ℓ ∞ , respectively. Furthermore, we speak of some inclusion relations and give the Schauder basis of the space ...

Properties and Riemann-Liouville fractional Hermite-Hadamard inequalities for the generalized ( α , m ) -preinvex functions

The authors first introduce the concepts of generalized ( α , m ) -preinvex function, generalized quasi m-preinvex function and explicitly ( α , m ) -preinvex function, and then provide some interesting properties for the newly introduced functions. The more important point is that we give a necessary and sufficient condition respecting the relationship between the generalized ( α ...

On the general K-interpolation method for the sum and the intersection

Let ( A 0 , A 1 ) be a compatible couple of normed spaces. We study the interrelation of the general K-interpolation spaces of the couple ( A 0 + A 1 , A 0 ∩ A 1 ) with those of the couples ( A 0 , A 1 ) , ( A 0 + A 1 , A 0 ) , ( A 0 + A 1 , A 1 ) , ( A 0 , A 0 ∩ A 1 ) , and ( A 1 , A 0 ∩ A 1 ) . MSC: 46B70.

On an implicit convexity concept and some integral inequalities

We introduce a new concept of convexity that depends on a function F : R × R × R × ( 0 , 1 ) → R satisfying certain axioms. The presented concept generalizes many kinds of convexity including ε-convex functions, α-convex functions, and h-convex functions. Moreover, some integral inequalities are provided via our notion of convexity. MSC: 26A51, 26D15, 35A23.

Some strong convergence properties for arrays of rowwise ANA random variables

In this paper, some complete convergence, complete moment convergence, and mean convergence results for arrays of rowwise asymptotically negatively associated (ANA) random variables are obtained. These theorems not only generalize some well-known ones to ANA cases, but they also improve them. MSC: 60F15, 60F25.

Operator iteration on the Young inequality

In this paper, we employ iteration on operator version of the famous Young inequality and obtain more arithmetic-geometric mean inequalities and the reverse versions for positive operators. Concretely, we obtain refined Young inequalities with the Kantorovich constant, the reverse ratio type and difference type inequalities for arithmetic-geometric operator mean under different ...

A certain ( p , q ) -derivative operator and associated divided differences

Recently, Sofonea (Gen. Math. 16:47-54, 2008 ) considered some relations in the context of quantum calculus associated with the q-derivative operator D q and divided difference. As applications of the post-quantum calculus known as the ( p , q ) -calculus, we derive several relations involving the ( p , q ) -derivative operator and divided differences. MSC: 11B68, 11B83, 81S40.

Boundedness of strong maximal functions with respect to non-doubling measures

The main purpose of this paper is to establish a boundedness result for strong maximal functions with respect to certain non-doubling measures in R n . More precisely, let d μ ( x 1 , … , x n ) = d μ 1 ( x 1 ) ⋯ d μ n ( x n ) be a product measure which is not necessarily doubling in R n (only assuming d μ i is doubling on R for i = 2 , … , n ), and let ω be a nonnegative and ...

On general partial Gaussian sums

Let q ≥ 2 be a fixed integer, A = A ( q ) ≤ q , B = B ( q ) ≤ q , and H = H ( q ) ≤ q . Define ħ ( A , B , H ) = { a ∈ Z ∣ ( a , q ) = 1 , a b ≡ 1 ( mod q ) , 1 ≤ a ≤ A , 1 ≤ b ≤ B , | a − b | ≤ H } . With the aid of the estimates for the general Kloosterman sums and the properties of trigonometric sums, we obtain an upper bound of the general partial Gaussian sums over the number ...

An alternative approach for a distance inequality associated with the second-order cone and the circular cone

It is well known that the second-order cone and the circular cone have many analogous properties. In particular, there exists an important distance inequality associated with the second-order cone and the circular cone. The inequality indicates that the distances of arbitrary points to the second-order cone and the circular cone are equivalent, which is crucial in analyzing the ...

Applications of anticipated BSDEs driven by time-changing Lévy noises

We study a very particular anticipated BSDEs when the driver is time-changing Lévy noise. We give an estimate of the solutions in the system satisfying some non-Lipschitz conditions. Also, we state an useful comparison theorem for the solutions. At last, we establish another specific Feynman-Kac formula for a quasilinear PDE.

Least-squares Hermitian problem of complex matrix equation ( A X B , C X D ) = ( E , F )

In this paper, we present a direct method to solve the least-squares Hermitian problem of the complex matrix equation ( A X B , C X D ) = ( E , F ) with complex arbitrary coefficient matrices A, B, C, D and the right-hand side E, F. This method determines the least-squares Hermitian solution with the minimum norm. It relies on a matrix-vector product and the Moore-Penrose ...

Boundedness of multidimensional Hausdorff operator on Hardy-Morrey and Besov-Morrey spaces

In this paper, we establish some boundedness conditions for the multidimensional Hausdorff operator on the homogeneous Hardy-Morrey and on the Besov-Morrey space, and we extend some results in the recent papers by Jia and Wang, and by Mazzucato, respectively. The main tool we implement in the study is the decomposition of the given function spaces in terms of atoms (smooth atoms ...

Coexistence of an unstirred chemostat model with B-D functional response by fixed point index theory

This paper deals with an unstirred chemostat model with the Beddington-DeAngelis functional response. First, some prior estimates for positive solutions are proved by the maximum principle and the method of upper and lower solutions. Second, the calculation on the fixed point index of chemostat model is obtained by degree theory and the homotopy invariance theorem. Finally, some ...

A necessary and sufficient condition for the inequality of generalized weighted means

We present in this paper a necessary and sufficient condition to establish the inequality between generalized weighted means which share the same sequence of numbers but differ in the weights. We first present a sufficient condition, and then obtain the more general, necessary and sufficient, condition. Our results were motivated by an inequality, involving harmonic means, found in ...

Bounded perturbation resilience of the viscosity algorithm

In this article, we investigate the bounded perturbation resilience of the viscosity algorithm and propose the superiorized version of the viscosity algorithm. The convergence of the proposed algorithm is analyzed for a nonexpansive mapping. A modified viscosity algorithm and its convergence is presented.

The convergence theorem for fourth-order super-Halley method in weaker conditions

In this paper, we establish the Newton-Kantorovich convergence theorem of a fourth-order super-Halley method under weaker conditions in Banach space, which is used to solve the nonlinear equations. Finally, some examples are provided to show the application of our theorem. MSC: 65J15, 65H10, 65G99, 47J25, 49M15.

On the general sum-connectivity index and general Randić index of cacti

Let G be a connected graph. The degree of a vertex x of G, denoted by d G ( x ) , is the number of edges adjacent to x. The general sum-connectivity index is the sum of the weights ( d G ( x ) + d G ( y ) ) α for all edges xy of G, where α is a real number. The general Randić index is the sum of weights of ( d G ( x ) d G ( y ) ) α for all edges xy of G, where α is a real number. ...

On the O ( 1 / t ) convergence rate of the alternating direction method with LQP regularization for solving structured variational inequality problems

In this paper, we propose a parallel descent LQP alternating direction method for solving structured variational inequality with three separable operators. The O ( 1 / t ) convergence rate for this method is studied. We also present some numerical examples to illustrate the efficiency of the proposed method. The results presented in this paper extend and improve some well-known ...

A characterization of nonhomogeneous wavelet dual frames in Sobolev spaces

In recent years, nonhomogeneous wavelet frames have attracted some mathematicians’ interest. This paper investigates such problems in a Sobolev space setting. A characterization of nonhomogeneous wavelet dual frames in Sobolev spaces pairs is obtained. MSC: 42C40, 42C15.

Bicyclic graphs with maximum sum of the two largest Laplacian eigenvalues

Let G be a simple connected graph and S 2 ( G ) be the sum of the two largest Laplacian eigenvalues of G. In this paper, we determine the bicyclic graph with maximum S 2 ( G ) among all bicyclic graphs of order n, which confirms the conjecture of Guan et al. (J. Inequal. Appl. 2014:242, 2014 ) for the case of bicyclic graphs. MSC: 05C50, 15A48.

Weak convergence theorem for variational inequality problems with monotone mapping in Hilbert space

We know that variational inequality problem is very important in the nonlinear analysis. The main purpose of this paper is to propose an iterative method for finding an element of the set of solutions of a variational inequality problem with a monotone and Lipschitz continuous mapping in Hilbert space. This iterative method is based on the extragradient method. We get a weak ...

Bounding the HL-index of a graph: a majorization approach

In mathematical chemistry, the median eigenvalues of the adjacency matrix of a molecular graph are strictly related to orbital energies and molecular orbitals. In this regard, the difference between the occupied orbital of highest energy (HOMO) and the unoccupied orbital of lowest energy (LUMO) has been investigated (see Fowler and Pisansky in Acta Chim. Slov. 57:513-517, 2010 ). ...

L p and BMO bounds for weighted Hardy operators on the Heisenberg group

In the setting of the Heisenberg group H n , we characterize those nonnegative functions w defined on [ 0 , 1 ] for which the weighted Hardy operator H w is bounded on L p ( H n ) , 1 ≤ p ≤ ∞ , and on BMO ( H n ) . Meanwhile, the corresponding operator norm in each case is derived. Furthermore, we introduce a type of weighted multilinear Hardy operators and obtain the ...