Journal of Inequalities and Applications

http://www.journalofinequalitiesandapplications.com/

List of Papers (Total 3,419)

Monotonicity, convexity, and inequalities for the generalized elliptic integrals

We provide the monotonicity and convexity properties and sharp bounds for the generalized elliptic integrals K a ( r ) $\mathscr{K}_{a}(r)$ and E a ( r ) $\mathscr {E}_{a}(r)$ depending on a parameter a ∈ ( 0 , 1 ) $a\in(0,1)$ , which contains an earlier result in the particular case a = 1 / 2 $a=1/2$ .

New results on reachable set bounding for linear time delay systems with polytopic uncertainties via novel inequalities

This work is further focused on analyzing a bound for a reachable set of linear uncertain systems with polytopic parameters. By means of L-K functional theory and novel inequalities, some new conditions which are expressed in the form of LMIs are derived. It should be noted that novel inequalities can improve upper bounds of Jensen inequalities, which yields less conservatism of ...

Chebyshev type inequalities by means of copulas

A copula is a function which joins (or ‘couples’) a bivariate distribution function to its marginal (one-dimensional) distribution functions. In this paper, we obtain Chebyshev type inequalities by utilising copulas.

New results on the continuous Weinstein wavelet transform

We consider the continuous wavelet transform S h W $\mathcal{S}_{h}^{W}$ associated with the Weinstein operator. We introduce the notion of localization operators for S h W $\mathcal {S}_{h}^{W}$ . In particular, we prove the boundedness and compactness of localization operators associated with the continuous wavelet transform. Next, we analyze the concentration of S h W ...

On the strong convergence for weighted sums of negatively superadditive dependent random variables

In this article, some strong convergence results for weighted sums of negatively superadditive dependent random variables are studied without assumption of identical distribution. The results not only generalize the corresponding ones of Cai (Metrika 68:323-331, 2008) and Sung (Stat. Pap. 52:447-454, 2011), but also extend and improve the corresponding one of Chen and Sung (Stat. ...

Fractional Hermite-Hadamard inequalities containing generalized Mittag-Leffler function

The objective of this paper is to establish some new refinements of fractional Hermite-Hadamard inequalities via a harmonically convex function with a kernel containing the generalized Mittag-Leffler function.

Nonexistence of global solutions of abstract wave equations with high energies

We consider an undamped second order in time evolution equation. For any positive value of the initial energy, we give sufficient conditions to conclude nonexistence of global solutions. The analysis is based on a differential inequality. The success of our result is based in a detailed analysis which is different from the ones commonly used to prove blow-up. Several examples are ...

Janowski type close-to-convex functions associated with conic regions

The analytic functions, mapping the open unit disk onto petal and oval type regions, introduced by Noor and Malik (Comput. Math. Appl. 62:2209-2217, 2011), are considered to define and study their associated close-to-convex functions. This work includes certain geometric properties like sufficiency criteria, coefficient estimates, arc length, the growth rate of coefficients of ...

A novel finite-time average consensus protocol based on event-triggered nonlinear control strategy for multiagent systems

We present a novel finite-time average consensus protocol based on event-triggered control strategy for multiagent systems. The system stability is proved. The lower bound of the interevent time is obtained to guarantee that there is no Zeno behavior. Moreover, the upper bound of the convergence time is obtained. The relationship between the convergence time and protocol parameter ...

Inequalities and asymptotics for some moment integrals

For α > β − 1 > 0 $\alpha>\beta-1>0$ , we obtain two-sided inequalities for the moment integral I ( α , β ) = ∫ R | x | − β | sin x | α d x $I(\alpha,\beta)=\int_{\mathbb{R}}|x|^{-\beta}|\sin x|^{\alpha}\,dx$ . These are then used to give the exact asymptotic behavior of the integral as α → ∞ $\alpha\rightarrow\infty$ . The case I ( α , α ) $I(\alpha,\alpha)$ corresponds to the ...

Optimal bounds for Neuman-Sándor mean in terms of the convex combination of the logarithmic and the second Seiffert means

In the article, we prove that the double inequality α L ( a , b ) + ( 1 − α ) T ( a , b ) 0 $a,b>0$ with a ≠ b $a\ne b $ if and only if α ≥ 1 / 4 $\alpha\ge1/4$ and β ≤ 1 − π / [ 4 log ( 1 + 2 ) ] $\beta\le1-\pi/[4\log(1+\sqrt{2})]$ , where NS ( a , b ) $\mathit{NS}(a,b)$ , L ( a , b ) $L(a,b)$ and T ( a , b ) $T(a,b)$ denote the Neuman-Sándor, logarithmic and second Seiffert means ...

Robust solutions to box-constrained stochastic linear variational inequality problem

We present a new method for solving the box-constrained stochastic linear variational inequality problem with three special types of uncertainty sets. Most previous methods, such as the expected value and expected residual minimization, need the probability distribution information of the stochastic variables. In contrast, we give the robust reformulation and reformulate the ...

On generalization of refinement of Jensen’s inequality using Fink’s identity and Abel-Gontscharoff Green function

In this paper, we formulate new Abel-Gontscharoff type identities involving new Green functions for the ‘two-point right focal’ problem. We use Fink’s identity and a new Abel-Gontscharoff-type Green’s function for a ‘two-point right focal’ to generalize the refinement of Jensen’s inequality given in (Horváth and Pečarić in Math. Inequal. Appl. 14: 777-791, 2011) from convex ...

A sharp Trudinger type inequality for harmonic functions and its applications

The present paper introduces a sharp Trudinger type inequality for harmonic functions based on the Cauchy-Riesz kernel function, which includes modified Poisson type kernel in a half plane considered by Xu et al. (Bound. Value Probl. 2013:262, 2013). As applications, we not only obtain Morrey representations of continuous linear maps for harmonic functions in the set of all closed ...

Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations

The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order 1 2 $\frac{1}{2}$ to SLSDDEs. On the one hand, the ...

An extended data envelopment analysis for the decision-making

Based on the CCR model, we propose an extended data envelopment analysis to evaluate the efficiency of decision making units with historical input and output data. The contributions of the work are threefold. First, the input and output data of the evaluated decision making unit are variable over time, and time series method is used to analyze and predict the data. Second, there ...

Primal-dual interior point QP-free algorithm for nonlinear constrained optimization

In this paper, a class of nonlinear constrained optimization problems with both inequality and equality constraints is discussed. Based on a simple and effective penalty parameter and the idea of primal-dual interior point methods, a QP-free algorithm for solving the discussed problems is presented. At each iteration, the algorithm needs to solve two or three reduced systems of ...

Quadratic convergence of monotone iterates for semilinear elliptic obstacle problems

In this paper, we consider the numerical solution for the discretization of semilinear elliptic complementarity problems. A monotone algorithm is established based on the upper and lower solutions of the problem. It is proved that iterates, generated by the algorithm, are a pair of upper and lower solution iterates and converge monotonically from above and below, respectively, to ...

On a new generalized symmetric vector equilibrium problem

In this paper, a new form of the symmetric vector equilibrium problem is introduced and, by mixing properties of the nonlinear scalarization mapping and the maximal element lemma, an existence theorem for it is established. We show that Ky Fan’s lemma, as a usual technique for proving the existence results for equilibrium problems, implies the maximal element lemma, while it is ...

Quantitative unique continuation for the linear coupled heat equations

In this paper, we established a quantitative unique continuation results for a coupled heat equations, with the homogeneous Dirichlet boundary condition, on a bounded convex domain Ω of R d $\mathbb{R}^{d}$ with smooth boundary ∂Ω. Our result shows that the value of the solutions can be determined uniquely by its value on an arbitrary open subset ω of Ω at any given positive time T.

Monotone and fast computation of Euler’s constant

We construct sequences of finite sums ( l ˜ n ) n ≥ 0 $(\tilde{l}_{n})_{n\geq 0}$ and ( u ˜ n ) n ≥ 0 $(\tilde{u}_{n})_{n\geq 0}$ converging increasingly and decreasingly, respectively, to the Euler-Mascheroni constant γ at the geometric rate 1/2. Such sequences are easy to compute and satisfy complete monotonicity-type properties. As a consequence, we obtain an infinite product ...