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Journal of Inequalities and Applications

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https://www.readbyqxmd.com/read/29780214/admissibility-of-simultaneous-prediction-for-actual-and-average-values-in-finite-population
#1
Chao Bai, Haiqi Li
This paper studies the admissibility of simultaneous prediction of actual and average values of the regressand in the generalized linear regression model under the quadratic loss function. Necessary and sufficient conditions are derived for the simultaneous prediction to be admissible in classes of homogeneous and nonhomogeneous linear predictors, respectively.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29780213/a-new-type-of-taylor-series-expansion
#2
Mohammad Masjed-Jamei, Zahra Moalemi, Iván Area, Juan J Nieto
We present a variant of the classical integration by parts to introduce a new type of Taylor series expansion and to present some closed forms for integrals involving Jacobi and Laguerre polynomials, which cannot be directly obtained by usual symbolic computation programs, i.e., only some very specific values can be computed by the mentioned programs. An error analysis is given in the sequel for the introduced expansion.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29780212/an-extended-reverse-hardy-hilbert-s-inequality-in-the-whole-plane
#3
Qiang Chen, Bicheng Yang
Using weight coefficients, a complex integral formula, and Hermite-Hadamard's inequality, we give an extended reverse Hardy-Hilbert's inequality in the whole plane with multiparameters and a best possible constant factor. Equivalent forms and a few particular cases are considered.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29780211/analysis-of-stability-for-stochastic-delay-integro-differential-equations
#4
Yu Zhang, Longsuo Li
In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step backward Euler method without any restriction on step-size, while the Euler-Maruyama method could reproduce the mean-square stability under a step-size constraint. We also confirm the mean-square stability of the split-step backward Euler method for nonlinear stochastic delay integro-differential equations...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29780210/a-conjugate-gradient-algorithm-for-large-scale-unconstrained-optimization-problems-and-nonlinear-equations
#5
Gonglin Yuan, Wujie Hu
For large-scale unconstrained optimization problems and nonlinear equations, we propose a new three-term conjugate gradient algorithm under the Yuan-Wei-Lu line search technique. It combines the steepest descent method with the famous conjugate gradient algorithm, which utilizes both the relevant function trait and the current point feature. It possesses the following properties: (i) the search direction has a sufficient descent feature and a trust region trait, and (ii) the proposed algorithm globally converges...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29773930/gradient-estimates-and-liouville-type-theorems-for-a-weighted-nonlinear-elliptic-equation
#6
Bingqing Ma, Yongli Dong
We consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a smooth metric measure space [Formula: see text]: [Formula: see text] where a , b are two real constants. When the ∞-Bakry-Émery Ricci curvature is bounded from below, we obtain a global gradient estimate which is not dependent on [Formula: see text]. In particular, we find that any bounded positive solution of the above equation must be constant under some suitable assumptions.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29773929/triple-diamond-alpha-integral-and-h%C3%A3-lder-type-inequalities
#7
Jing-Feng Tian
In this paper, we first introduce the definition of triple Diamond-Alpha integral for functions of three variables. Therefore, we present the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral on time scales, and then we obtain some new generalizations of the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral. Moreover, using the obtained results, we give a new generalization of the Minkowski inequality for the triple Diamond-Alpha integral on time scales...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29773928/multiplicity-and-asymptotic-behavior-of-solutions-to-a-class-of-kirchhoff-type-equations-involving-the-fractional-p-laplacian
#8
Liejun Shen
The present study is concerned with the following fractional p -Laplacian equation involving a critical Sobolev exponent of Kirchhoff type: [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are constants, and [Formula: see text] is the fractional p -Laplacian operator with [Formula: see text] and [Formula: see text]. For suitable [Formula: see text], the above equation possesses at least two nontrivial solutions by variational method for any [Formula: see text]. Moreover, we regard [Formula: see text] and [Formula: see text] as parameters to obtain convergent properties of solutions for the given problem as [Formula: see text] and [Formula: see text], respectively...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29769791/refined-wirtinger-type-integral-inequality
#9
Liansheng Zhang, Shuxia Wang
Based on the extreme value conditions of a multiple variables function, a new class of Wirtinger-type double integral inequality is established in this paper. The proposed inequality generalizes and refines the classical Wirtinger-based integral inequality and has less conservatism in comparison with Jensen's double integral inequality and other double integral inequalities in the literature. Thus, the stability criteria for delayed control systems derived by the proposed refined Wirtinger-type integral inequality are less conservative than existing results in the literature...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29769790/a-class-of-derivative-free-trust-region-methods-with-interior-backtracking-technique-for-nonlinear-optimization-problems-subject-to-linear-inequality-constraints
#10
Jing Gao, Jian Cao
This paper focuses on a class of nonlinear optimization subject to linear inequality constraints with unavailable-derivative objective functions. We propose a derivative-free trust-region methods with interior backtracking technique for this optimization. The proposed algorithm has four properties. Firstly, the derivative-free strategy is applied to reduce the algorithm's requirement for first- or second-order derivatives information. Secondly, an interior backtracking technique ensures not only to reduce the number of iterations for solving trust-region subproblem but also the global convergence to standard stationary points...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29769789/-formula-see-text-convergence-complete-convergence-and-weak-laws-of-large-numbers-for-asymptotically-negatively-associated-random-vectors-with-values-in-formula-see-text
#11
Mi-Hwa Ko
In this paper, based on the Rosenthal-type inequality for asymptotically negatively associated random vectors with values in [Formula: see text], we establish results on [Formula: see text]-convergence and complete convergence of the maximums of partial sums are established. We also obtain weak laws of large numbers for coordinatewise asymptotically negatively associated random vectors with values in [Formula: see text].
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29769788/new-bounds-for-the-exponential-function-with-cotangent
#12
Ling Zhu
In this paper, new bounds for the exponential function with cotangent are found by using the recurrence relation between coefficients in the expansion of power series of the function [Formula: see text] and a new criterion for the monotonicity of the quotient of two power series.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29755245/a-new-smoothing-modified-three-term-conjugate-gradient-method-for-formula-see-text-norm-minimization-problem
#13
Shouqiang Du, Miao Chen
We consider a kind of nonsmooth optimization problems with [Formula: see text]-norm minimization, which has many applications in compressed sensing, signal reconstruction, and the related engineering problems. Using smoothing approximate techniques, this kind of nonsmooth optimization problem can be transformed into a general unconstrained optimization problem, which can be solved by the proposed smoothing modified three-term conjugate gradient method. The smoothing modified three-term conjugate gradient method is based on Polak-Ribière-Polyak conjugate gradient method...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29755244/genuine-modified-bernstein-durrmeyer-operators
#14
Syed Abdul Mohiuddine, Tuncer Acar, Mohammed A Alghamdi
The present paper deals with genuine Bernstein-Durrmeyer operators which preserve some certain functions. The rate of convergence of new operators via a Peetre [Formula: see text]-functional and corresponding modulus of smoothness, quantitative Voronovskaya type theorem and Grüss-Voronovskaya type theorem in quantitative mean are discussed. Finally, the graphic for new operators with special cases and for some values of n is also presented.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29755243/strong-convergence-and-bounded-perturbation-resilience-of-a-modified-proximal-gradient-algorithm
#15
Yanni Guo, Wei Cui
The proximal gradient algorithm is an appealing approach in finding solutions of non-smooth composite optimization problems, which may only has weak convergence in the infinite-dimensional setting. In this paper, we introduce a modified proximal gradient algorithm with outer perturbations in Hilbert space and prove that the algorithm converges strongly to a solution of the composite optimization problem. We also discuss the bounded perturbation resilience of the basic algorithm of this iterative scheme and illustrate it with an application...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29720848/existence-of-weak-solutions-of-stochastic-delay-differential-systems-with-schr%C3%A3-dinger-brownian-motions
#16
Jianguo Sun, Liang Kou, Gang Guo, Guodong Zhao, Yong Wang
By using new Schrödinger type inequalities appearing in Jiang and Usó (J. Inequal. Appl. 2016:233, 2016), we study the existence of weak solutions of stochastic delay differential systems with Schrödinger-Brownian motions.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29720847/on-kedlaya-type-inequalities-for-weighted-means
#17
Zsolt Páles, Paweł Pasteczka
In 2016 we proved that for every symmetric, repetition invariant and Jensen concave mean [Formula: see text] the Kedlaya-type inequality [Formula: see text] holds for an arbitrary [Formula: see text] ([Formula: see text] stands for the arithmetic mean). We are going to prove the weighted counterpart of this inequality. More precisely, if [Formula: see text] is a vector with corresponding (non-normalized) weights [Formula: see text] and [Formula: see text] denotes the weighted mean then, under analogous conditions on [Formula: see text], the inequality [Formula: see text] holds for every [Formula: see text] and [Formula: see text] such that the sequence [Formula: see text] is decreasing...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29720846/sherman-s-and-related-inequalities-with-applications-in-information-theory
#18
S Ivelić Bradanović, N Latif, Ð Pečarić, J Pečarić
In this paper we give extensions of Sherman's inequality considering the class of convex functions of higher order. As particular cases, we get an extended weighted majorization inequality as well as Jensen's inequality which have direct connection to information theory. We use the obtained results to derive new estimates for Shannon's and Rényi's entropy, information energy, and some well-known measures between probability distributions. Using the Zipf-Mandelbrot law, we introduce new functionals to derive some related results...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29720845/a-cauchy-type-inequality-for-m%C3%A3-bius-operations
#19
Keiichi Watanabe
In this article, we show two fundamental features of the restriction of Möbius operations to the real numbers, that is, a Cauchy type inequality and a criterion for convergence of series.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29720844/a-law-of-iterated-logarithm-for-the-subfractional-brownian-motion-and-an-application
#20
Hongsheng Qi, Litan Yan
Let [Formula: see text] be a sub-fractional Brownian motion with Hurst index [Formula: see text]. In this paper, we give a local law of the iterated logarithm of the form [Formula: see text] almost surely, for all [Formula: see text], where [Formula: see text] for [Formula: see text]. As an application, we introduce the [Formula: see text]-variation of [Formula: see text] driven by [Formula: see text] [Formula: see text] with [Formula: see text].
2018: Journal of Inequalities and Applications
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