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Journal of Inequalities and Applications

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https://www.readbyqxmd.com/read/30137923/on-the-preconditioned-gaor-method-for-a-linear-complementarity-problem-with-an-m-matrix
#1
Shu-Xin Miao, Dan Zhang
Recently, based on the Hadjidimos preconditioner, a preconditioned GAOR method was proposed for solving the linear complementarity problem (Liu and Li in East Asian J. Appl. Math. 2:94-107, 2012). In this paper, we propose a new preconditioned GAOR method for solving the linear complementarity problem with an M -matrix. The convergence of the proposed method is analyzed, and the comparison results are obtained to show it accelerates the convergence of the original GAOR method and the preconditioned GAOR method in (Liu and Li in East Asian J...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137922/a-note-on-the-almost-schur-lemma-on-smooth-metric-measure-spaces
#2
Jui-Tang Chen
In this paper, we prove almost-Schur inequalities on closed smooth metric measure spaces, which implies the results of Cheng and De Lellis-Topping whenever the weighted function f is constant.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137921/an-improved-approach-for-studying-oscillation-of-second-order-neutral-delay-differential-equations
#3
Said R Grace, Jozef Džurina, Irena Jadlovská, Tongxing Li
The paper is devoted to the study of oscillation of solutions to a class of second-order half-linear neutral differential equations with delayed arguments. New oscillation criteria are established, and they essentially improve the well-known results reported in the literature, including those for non-neutral differential equations. The adopted approach refines the classical Riccati transformation technique by taking into account such part of the overall impact of the delay that has been neglected in the earlier results...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137920/characterization-and-stability-of-approximately-dual-g-frames-in-hilbert-spaces
#4
Yan-Ling Fu, Wei Zhang
This paper addresses approximately dual g-frames. First, we establish a connection between approximately dual g-frames and dual g-frames and obtain a characterization of approximately dual g-frames. Second, we give results on stability of approximately dual g-frames, which cover the results obtained by other authors.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137919/spectral-properties-of-an-impulsive-sturm-liouville-operator
#5
Elgiz Bairamov, Ibrahim Erdal, Seyhmus Yardimci
This work is devoted to discuss some spectral properties and the scattering function of the impulsive operator generated by the Sturm-Liouville equation. We present a different method to investigate the spectral singularities and eigenvalues of the mentioned operator. We also obtain the finiteness of eigenvalues and spectral singularities with finite multiplicities under some certain conditions. Finally, we illustrate our results by a detailed example.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137918/metric-characterizations-for-well-posedness-of-split-hemivariational-inequalities
#6
Qiao-Yuan Shu, Rong Hu, Yi-Bin Xiao
In this paper, we generalize the concept of well-posedness to a class of split hemivariational inequalities. By imposing very mild assumptions on involved operators, we establish some metric characterizations of the well-posedness for the split hemivariational inequality. The obtained results generalize some related theorems on well-posedness for hemivariational inequalities and variational inequalities in the literature.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137917/wavelet-density-estimation-for-mixing-and-size-biased-data
#7
Junke Kou, Huijun Guo
This paper considers wavelet estimation for a multivariate density function based on mixing and size-biased data. We provide upper bounds for the mean integrated squared error (MISE) of wavelet estimators. It turns out that our results reduce to the corresponding theorem of Shirazi and Doosti (Stat. Methodol. 27:12-19, 2015), when the random sample is independent.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137916/estimates-for-iterated-commutators-of-multilinear-square-fucntions-with-dini-type-kernels
#8
Zengyan Si, Qingying Xue
Let <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi>Π</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>→</mml:mo> </mml:mover> </mml:mrow> </mml:msub> </mml:math> be the commutator generated by a multilinear square function and Lipschitz functions with kernel satisfying Dini-type condition. We show that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi>Π</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>→</mml:mo> </mml:mover> </mml:mrow> </mml:msub> </mml:math> is bounded from product Lebesgue spaces into Lebesgue spaces, Lipschitz spaces, and Triebel-Lizorkin spaces...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137915/well-posedness-for-a-class-of-generalized-variational-hemivariational-inequalities-involving-set-valued-operators
#9
Caijing Jiang
The aim of present work is to study some kinds of well-posedness for a class of generalized variational-hemivariational inequality problems involving set-valued operators. Some systematic approaches are presented to establish some equivalence theorems between several classes of well-posedness for the inequality problems and some corresponding metric characterizations, which generalize many known results. Finally, the well-posedness for a class of generalized mixed equilibrium problems is also considered.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137914/covering-functionals-of-cones-and-double-cones
#10
Senlin Wu, Ke Xu
The least positive number γ such that a convex body K can be covered by m translates of γK is called the covering functional of K (with respect to m ), and it is denoted by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Γ</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:mo>(</mml:mo> <mml:mi>K</mml:mi> <mml:mo>)</mml:mo> </mml:math> . Estimating covering functionals of convex bodies is an important part of Chuanming Zong's quantitative program for attacking Hadwiger's covering conjecture...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137913/the-growth-and-approximation-for-an-analytic-function-represented-by-laplace-stieltjes-transforms-with-generalized-order-converging-in-the-half-plane
#11
Hong Yan Xu, Hua Wang
By utilizing the concept of generalized order, we investigate the growth of Laplace-Stieltjes transform converging in the half plane and obtain one equivalence theorem concerning the generalized order of Laplace-Stieltjes transforms. Besides, we also study the problem on the approximation of this Laplace-Stieltjes transform and give some results about the generalized order, the error, and the coefficients of Laplace-Stieltjes transforms. Our results are extension and improvement of the previous theorems given by Luo and Kong, Singhal, and Srivastava...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137912/on-a-new-discrete-mulholland-type-inequality-in-the-whole-plane
#12
Bicheng Yang, Qiang Chen
A new discrete Mulholland-type inequality in the whole plane with a best possible constant factor is presented by introducing multi-parameters, applying weight coefficients, and using Hermite-Hadamard's inequality. Moreover, the equivalent forms, some particular cases, and the operator expressions are considered.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137911/some-generalizations-of-inequalities-for-sector-matrices
#13
Chaojun Yang, Fangyan Lu
In this paper, we generalize some Schatten p -norm inequalities for accretive-dissipative matrices obtained by Kittaneh and Sakkijha. Moreover, we present some inequalities for sector matrices.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137910/some-notes-about-one-inequality-with-power-functions
#14
Ladislav Matejíčka
In this paper, we prove one inequality with power functions. A simplified form of the inequality was published as the problem 12024-02 in the American Mathematical Monthly.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137909/approximate-weakly-efficient-solutions-of-set-valued-vector-equilibrium-problems
#15
Jian Chen, Yihong Xu, Ke Zhang
In this paper, we introduce a new kind of approximate weakly efficient solutions to the set-valued vector equilibrium problems with constraints in locally convex Hausdorff topological vector spaces; then we discuss a relationship between the weakly efficient solutions and approximate weakly efficient solutions. Under the assumption of near cone-subconvexlikeness, by using the separation theorem for convex sets we establish Kuhn-Tucker-type and Lagrange-type optimality conditions for set-valued vector equilibrium problems, respectively...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137908/maximum-norm-error-estimates-of-fourth-order-compact-difference-scheme-for-the-nonlinear-schr%C3%A3-dinger-equation-involving-a-quintic-term
#16
Hanqing Hu, Hanzhang Hu
A compact finite difference (CFD) scheme is presented for the nonlinear Schrödinger equation involving a quintic term. The two discrete conservative laws are obtained. The unconditional stability and convergence in maximum norm with order <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>τ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> <mml:mi>h</mml:mi> <mml:mn>4</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:math> are proved by using the energy method...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137907/simple-form-of-a-projection-set-in-hybrid-iterative-schemes-for-non-linear-mappings-application-of-inequalities-and-computational-experiments
#17
Li Wei, Ravi P Agarwal
Some relaxed hybrid iterative schemes for approximating a common element of the sets of zeros of infinite maximal monotone operators and the sets of fixed points of infinite weakly relatively non-expansive mappings in a real Banach space are presented. Under mild assumptions, some strong convergence theorems are proved. Compared to recent work, two new projection sets are constructed, which avoids calculating infinite projection sets for each iterative step. Some inequalities are employed sufficiently to show the convergence of the iterative sequences...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137906/an-accelerating-algorithm-for-globally-solving-nonconvex-quadratic-programming
#18
Li Ge, Sanyang Liu
To globally solve a nonconvex quadratic programming problem, this paper presents an accelerating linearizing algorithm based on the framework of the branch-and-bound method. By utilizing a new linear relaxation approach, the initial quadratic programming problem is reduced to a sequence of linear relaxation programming problems, which is used to obtain a lower bound of the optimal value of this problem. Then, by using the deleting operation of the investigated regions, we can improve the convergent speed of the proposed algorithm...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137905/a-new-version-of-carleson-measure-associated-with-hermite-operator
#19
Jizheng Huang, Yaqiong Wang, Weiwei Li
Let <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>L</mml:mi> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mi>Δ</mml:mi> <mml:mo>+</mml:mo> <mml:msup> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>x</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:math> be a Hermite operator, where Δ is the Laplacian on <mml:math xmlns:mml="http://www...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30137904/inequalities-for-the-fractional-convolution-operator-on-differential-forms
#20
Zhimin Dai, Huacan Li, Qunfang Li
The purpose of this paper is to derive some Coifman type inequalities for the fractional convolution operator applied to differential forms. The Lipschitz norm and BMO norm estimates for this integral type operator acting on differential forms are also obtained.
2018: Journal of Inequalities and Applications
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