Sharp remainder terms are explicitly given on the standard Hardy inequalities in L p ( R n ) with 1 < p < n . Those remainder terms provide a direct and exact understanding of Hardy type inequalities in the framework of equalities as well as of the nonexistence of nontrivial extremals. MSC: 26D10, 26D15, 46E35.

In this paper, we first introduce some new Morrey-type spaces containing generalized Morrey space and weighted Morrey space with two weights as special cases. Then we give the weighted strong type and weak type estimates for fractional integral operators I α in these new Morrey-type spaces. Furthermore, the weighted strong type estimate and endpoint estimate of linear commutators [ ...

In this study, the simplex whose vertices are barycenters of the given simplex facets plays an essential role. The article provides an extension of the Hermite-Hadamard inequality from the simplex barycenter to any point of the inscribed simplex except its vertices. A two-sided refinement of the generalized inequality is obtained in completion of this work. MSC: 26B25, 52A40.

We derive the Levinson type generalization of the Jensen and the converse Jensen inequality for real Stieltjes measure, not necessarily positive. As a consequence, also the Levinson type generalization of the Hermite-Hadamard inequality is obtained. Similarly, we derive the Levinson type generalization of Giaccardi’s inequality. The obtained results are then applied for ...

In many applications, the available data come from a sampling scheme that causes loss of information in terms of left truncation. In some cases, in addition to left truncation, the data are weakly dependent. In this paper we are interested in deriving the asymptotic normality as well as a Berry-Esseen type bound for the kernel density estimator of left truncated and weakly ...

This paper formulates an infected predator-prey model with Beddington-DeAngelis functional response from a classical deterministic framework to a stochastic differential equation (SDE). First, we provide a global analysis including the global positive solution, stochastically ultimate boundedness, the persistence in mean, and extinction of the SDE system by using the technique of a ...

In this article, some new oscillation criterion for the second order Emden-Fowler functional differential equation of neutral type ( r ( t ) | z ′ ( t ) | α − 1 z ′ ( t ) ) ′ + q ( t ) | x ( σ ( t ) ) | β − 1 x ( σ ( t ) ) = 0 , where z ( t ) = x ( t ) + p ( t ) x ( τ ( t ) ) , α > 0 and β > 0 are established. Our results improve some well-known results which were published ...

The uniqueness of the solution for the definite problem of a parabolic variational inequality is proved. The problem comes from the study of the optimal exercise strategies for the perpetual executive stock options with unrestricted exercise in financial market. Because the variational inequality is degenerate and the obstacle condition contains the partial derivative of an unknown ...

This paper is purported to investigate a food chain reaction-diffusion predator-prey system with nonlocal delays in a bounded domain with no flux boundary condition. We investigate the global stability and find the sufficient conditions of global stability of the unique positive equilibrium for this system. The derived results show that delays often restrain stability. Using the ...

Conjugate gradient methods play an important role in many fields of application due to their simplicity, low memory requirements, and global convergence properties. In this paper, we propose an efficient three-term conjugate gradient method by utilizing the DFP update for the inverse Hessian approximation which satisfies both the sufficient descent and the conjugacy conditions. The ...

We establish characterizations of both boundedness and of compactness of a general class of fractional integral operators involving the Riemann-Liouville, Hadamard, and Erdelyi-Kober operators. In particular, these results imply new results in the theory of Hardy type inequalities. As applications both new and well-known results are pointed out. MSC: 26A33, 26D10, 47G10.

In the article, we provide the necessary and sufficient conditions for the parameters α and β such that the generalized Wilker-type inequality 2 β α + 2 β ( sin x x ) α + α α + 2 β ( tan x x ) β − 1 > ( < ) 0 holds for all x ∈ ( 0 , π / 2 ) . MSC: 26D05, 33B10.

Based on the Padé approximation method, we present new inequalities for Gauss lemniscate functions. We also solve a conjecture on inequalities for Gauss lemniscate functions proposed by Sun and Chen. MSC: 26D07, 41A60.

We study the asymptotic properties of the solutions of a class of even-order damped differential equations with p-Laplacian like operators, delayed and advanced arguments. We present new theorems that improve and complement related contributions reported in the literature. Several examples are provided to illustrate the practicability, maneuverability, and efficiency of the results ...

In this paper, we give the notion of locally convex probabilistic seminormed spaces and discuss some property of locally convex probabilistic seminormed spaces. MSC: 4E70, 46S50.

In this paper we introduce q-Szász-Mirakjan-Kantorovich operators generated by a Dunkl generalization of the exponential function and we propose two different modifications of the q-Szász-Mirakjan-Kantorovich operators which preserve some test functions. We obtain some approximation results with the help of the well-known Korovkin theorem and the weighted Korovkin theorem for these ...

In this paper, we obtain an extended Halanay inequality with unbounded coefficient functions on time scales, which extends an earlier result in Wen et al. (J. Math. Anal. Appl. 347:169-178, 2008 ). Two illustrative examples are also given.

We consider the extremal problem of maximizing functions u in the class of real-valued biconvex functions satisfying a boundary condition ψ on a product of the unit ball with itself, with the ℓ p -norm. In 1986, Burkholder explicitly found the maximal function for p = 2 . In this paper, we find some characterizations of such extremal functions. We establish that sufficiently smooth ...

In this paper, we study the complete moment convergence of the sums of ρ̃-mixing sequences which are double-indexed randomly weighted and stochastically dominated by a random variable X. Under the different moment conditions on X and weights, many complete moment convergence and complete convergence results are obtained. Moreover, some simulations are given for illustration. MSC: ...

In this paper, we define a geometric circulant matrix whose entries are the generalized Fibonacci numbers and hyperharmonic Fibonacci numbers. Then we give upper and lower bounds for the spectral norms of these matrices. MSC: 15A60, 11B39, 15B05.

In this paper, we introduce the binomial sequence spaces b 0 r , s and b c r , s of nonabsolute type which include the spaces c 0 and c, respectively. Also, we prove that the spaces b 0 r , s and b c r , s are linearly isomorphic to the spaces c 0 and c, in turn, and we investigate some inclusion relations. Moreover, we obtain the Schauder bases of those spaces and determine their ...

In the article, we present the necessary and sufficient condition for the parameter p on the interval ( 7 / 5 , ∞ ) such that the function x → erf ( x ) / B p ( x ) is strictly increasing (decreasing) on ( 0 , ∞ ) , and find the best possible parameters p, q on the interval ( 7 / 5 , ∞ ) such that the double inequality B p ( x ) < erf ( x ) < B q ( x ) holds for all x > 0 , where ...

Let W = λ B + ν B H be a mixed-fractional Brownian motion with Hurst index 0 < H < 1 2 and λ , ν ≠ 0 . In this paper we study the quadratic covariation [ f ( W ) , W ] ( H ) defined by [ f ( W ) , W ] t ( H ) : = lim ε ↓ 0 1 ν 2 ε 2 H ∫ 0 t { f ( W s + ε ) − f ( W s ) } ( W s + ε − W s ) d η s in probability, where f is a Borel function and η s = λ 2 s + ν 2 s 2 H . For some ...

This paper is concerned with upper Hölder continuity and Hölder calmness of a perturbed vector optimization problem. We establish some new sufficient conditions for upper Hölder continuity and Hölder calmness of the perturbed solution mappings and the perturbed optimal value mappings of a vector optimization problem under the case that the objective function and the feasible set ...

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.