Journal of Inequalities and Applications

List of Papers (Total 3,385)

Inner approximation algorithm for generalized linear multiplicative programming problems

An efficient inner approximation algorithm is presented for solving the generalized linear multiplicative programming problem with generalized linear multiplicative constraints. The problem is firstly converted into an equivalent generalized geometric programming problem, then some magnifying-shrinking skills and approximation strategies are used to convert the equivalent...

Global maximal inequality to a class of oscillatory integrals

In the present paper, we give the global L q $L^{q}$ estimates for maximal operators generated by multiparameter oscillatory integral S t , Φ $S_{t,\varPhi}$ , which is defined by S t , Φ f ( x ) = ( 2 π ) − n ∫ R n e i x ⋅ ξ e i ( t 1 ϕ 1 ( | ξ 1 | ) + t 2 ϕ 2 ( | ξ 2 | ) + ⋯ + t n ϕ n ( | ξ n | ) ) f ˆ ( ξ ) d ξ , x ∈ R n , $$S_{t,\varPhi}f(x)=(2\pi)^{-n} \int_{\mathbb{R}^{n...

On properties of geodesic semilocal E-preinvex functions

The authors define a class of functions on Riemannian manifolds, which are called geodesic semilocal E-preinvex functions, as a generalization of geodesic semilocal E-convex and geodesic semi E-preinvex functions, and some of its properties are established. Furthermore, a nonlinear fractional multiobjective programming is considered, where the functions involved are geodesic E...

Some inequalities for Cesàro means of double Vilenkin–Fourier series

In this paper, we state and prove some new inequalities related to the rate of L p $L^{p}$ approximation by Cesàro means of the quadratic partial sums of double Vilenkin–Fourier series of functions from L p $L^{p}$ .

On a result of Cartwright and Field

Let M n , r = ( ∑ i = 1 n q i x i r ) 1 r $M_{n,r}=(\sum_{i=1}^{n}q_{i}x_{i}^{r})^{\frac{1}{r}}$ , r ≠ 0 $r\neq 0$ , and M n , 0 = lim r → 0 M n , r $M_{n,0}= \lim_{r \rightarrow 0}M_{n,r}$ be the weighted power means of n non-negative numbers x i $x_{i}$ , 1 ≤ i ≤ n $1 \leq i \leq n$ , with q i > 0 $q_{i} > 0$ satisfying ∑ i = 1 n q i = 1 $\sum^{n}_{i=1}q_{i}=1$ . For r > s $r>s...

Opial inequality in q -calculus

In this article we give q-analogs of the Opial inequality for q-decreasing functions. Using a closed form of the restricted q-integral (see Gauchman in Comput. Math. Appl. 47:281–300, 2004), we establish a new integral inequality of the q-Opial type.

Bohr-type inequalities of analytic functions

In this paper, we investigate the Bohr-type radii for several different forms of Bohr-type inequalities of analytic functions in the unit disk, we also investigate the Bohr-type radius of the alternating series associated with the Taylor series of analytic functions. We will prove that most of the results are sharp.

A tensor trust-region model for nonlinear system

It has turned out that the tensor expansion model has better approximation to the objective function than models of the normal second Taylor expansion. This paper conducts a study of the tensor model for nonlinear equations and it includes the following: (i) a three dimensional symmetric tensor trust-region subproblem model of the nonlinear equations is presented; (ii) the three...

About the sharpness of the Jensen inequality

The main aim of this paper is to give an improvement of the recent result on the sharpness of the Jensen inequality. The results given here are obtained using different Green functions and considering the case of the real Stieltjes measure, not necessarily positive. Finally, some applications involving various types of f-divergences and Zipf–Mandelbrot law are presented.

Relaxed alternating CQ algorithms for the split equality problem in Hilbert spaces

In this paper, we are concerned with the split equality problem (SEP) in Hilbert spaces. By converting it to a coupled fixed-point equation, we propose a new algorithm for solving the SEP. Whenever the convex sets involved are level sets of given convex functionals, we propose two new relaxed alternating algorithms for the SEP. The first relaxed algorithm is shown to be weakly...

Improved McClelland and Koolen–Moulton bounds for distance energy of a graph

Let G be a graph with n vertices and m edges. The term energy of a graph G was introduced by I. Gutman in chemistry due to its relevance to the total π-electron energy of a carbon compound. An analogous energy E D ( G ) $\mathcal{E}_{D}(G)$ , called the distance energy, was defined by Indulal et al. (MATCH Commun. Math. Comput. Chem. 60:461–472, 2008) in 2008. McClelland and...

Certain new bounds considering the weighted Simpson-like type inequality and applications

We investigate a weighted Simpson-type identity and obtain new estimation-type results related to the weighted Simpson-like type inequality for the first-order differentiable mappings. We also present some applications to f-divergence measures and to higher moments of continuous random variables.

Shrinkage estimation of non-negative mean vector with unknown covariance under balance loss

Parameter estimation in multivariate analysis is important, particularly when parameter space is restricted. Among different methods, the shrinkage estimation is of interest. In this article we consider the problem of estimating the p-dimensional mean vector in spherically symmetric models. A dominant class of Baranchik-type shrinkage estimators is developed that outperforms the...

Stability criteria on delay-dependent robust stability for uncertain neutral stochastic nonlinear systems with time-delay

This work mainly studies the robust stability analysis and design of a controller for uncertain neutral stochastic nonlinear systems with time-delay. Using a modified Lyapunov–Krasovskii functional and the free-weighting matrices technique, we establish some new delay-dependent criteria in terms of linear matrix inequality (LMI). The innovative point of this work is that we...

Large deviation principle for the mean reflected stochastic differential equation with jumps

In this paper, we establish a large deviation principle for a mean reflected stochastic differential equation driven by both Brownian motion and Poisson random measure. The weak convergence method plays an important role.

Some limit properties for a hidden inhomogeneous Markov chain

This paper presents a general strong limit theorem for delayed sum of functions of random variables for a hidden time inhomogeneous Markov chain (HTIMC), and as corollaries, some strong laws of large numbers for HTIMC are established thereby.

AE solutions to two-sided interval linear systems over max-plus algebra

This paper introduces a concept of AE solutions to two-sided interval max-plus linear systems, a rather general concept which includes many known concepts of solutions to interval systems, in particular, weak, strong, tolerance and control solutions as its special cases. We state full characterizations of AE solutions for the two-sided interval max-plus systems, including both...

Approximation formulas related to Somos’ quadratic recurrence constant

We present two classes of asymptotic expansions related to Somos’ quadratic recurrence constant and provide the recursive relations for determining the coefficients of each class of the asymptotic expansions by using Bell polynomials and other techniques. We also present continued fraction approximations related to Somos’ quadratic recurrence constant.

Geometric inequalities for warped product bi-slant submanifolds with a warping function

In this paper, we prove that the squared norm of the second fundamental form for bi-slant submanifolds with any codimension of nearly trans-Sasakian manifolds is bounded below by the gradient of a warping function and also find the conditions on which the equality holds. Some related examples are also provided.

Different types of quantum integral inequalities via ( α , m ) $(\alpha ,m)$ -convexity

In this paper, based on ( α , m ) $(\alpha,m)$ -convexity, we establish different type inequalities via quantum integrals. These inequalities generalize some results given in the literature.

Monotonicity of the number of positive entries in nonnegative matrix powers

Let A be a nonnegative matrix of order n and f ( A ) $f(A)$ denote the number of positive entries in A. We prove that if f ( A ) ≤ 3 $f(A)\leq3$ or f ( A ) ≥ n 2 − 2 n + 2 $f(A)\geq n^{2}-2n+2$ , then the sequence { f ( A k ) } k = 1 ∞ $\{f(A^{k})\}_{k=1}^{\infty}$ is monotonic for positive integers k.

Quadratic transformation inequalities for Gaussian hypergeometric function

In the article, we present several quadratic transformation inequalities for Gaussian hypergeometric function and find the analogs of duplication inequalities for the generalized Grötzsch ring function.

New generalized systems of nonlinear ordered variational inclusions involving ⊕ operator in real ordered Hilbert spaces

This manuscript deals with two general systems of nonlinear ordered variational inclusion problems. We also construct some new iterative algorithms for finding approximation solutions to the general systems of nonlinear ordered variational inclusions and prove the convergence of the sequences obtained by the schemes. The results presented in the manuscript are new and improve...

Inequalities involving hypergeometric and related functions

An inequality is being proved which is connected to cost-effective numerical density estimation of the hyper-gamma probability distribution. The left-hand side of the inequality is a combination of two in the third parameter distinct versions of the hypergeometric function at the point one. All three parameters are functions of the distribution’s terminal shape. The first and...