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Journal of Inequalities and Applications

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https://www.readbyqxmd.com/read/30008537/refining-trigonometric-inequalities-by-using-pad%C3%A3-approximant
#1
Zhen Zhang, Huaqing Shan, Ligeng Chen
A two-point Padé approximant method is presented for refining some remarkable trigonometric inequalities including the Jordan inequality, Kober inequality, Becker-Stark inequality, and Wu-Srivastava inequality. Simple proofs are provided. It shows to achieve better approximation results than those of prevailing methods.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30008536/sums-of-finite-products-of-chebyshev-polynomials-of-the-second-kind-and-of-fibonacci-polynomials
#2
Taekyun Kim, Dae San Kim, Dmitry V Dolgy, Jin-Woo Park
In this paper, we consider sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials and derive Fourier series expansions of functions associated with them. From these Fourier series expansions, we can express those sums of finite products in terms of Bernoulli polynomials and obtain some identities by using those expressions.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30008535/inequalities-and-asymptotic-expansions-related-to-the-generalized-somos-quadratic-recurrence-constant
#3
Xue-Si Ma, Chao-Ping Chen
In this paper, we give asymptotic expansions and inequalities related to the generalized Somos quadratic recurrence constant, using its relation with the generalized Euler constant.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30008534/some-majorization-integral-inequalities-for-functions-defined-on-rectangles
#4
Shanhe Wu, Muhammad Adil Khan, Abdul Basir, Reza Saadati
In this paper, we first prove an integral majorization theorem related to integral inequalities for functions defined on rectangles. We then apply the result to establish some new integral inequalities for functions defined on rectangles. The results obtained are generalizations of weighted Favard's inequality, which also provide a generalization of the results given by Maligranda et al. (J. Math. Anal. Appl. 190:248-262, 1995) in an earlier paper.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/30008533/some-generalizations-of-the-new-sor-like-method-for-solving-symmetric-saddle-point-problems
#5
Ruiping Wen, Ruihuan Wu, Jinrui Guan
Saddle-point problems arise in many areas of scientific computing and engineering applications. Research on the efficient numerical methods of these problems has become a hot topic in recent years. In this paper, we propose some generalizations of the new SOR-like method based on the original method. Convergence of these methods is discussed under suitable restrictions on iteration parameters. Numerical experiments are given to show that these methods are effective and efficient.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29973772/generalization-of-the-space-l-p-derived-by-absolute-euler-summability-and-matrix-operators
#6
Fadime Gökçe, Mehmet Ali Sarıgöl
The sequence space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>l</mml:mi> <mml:mo>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>)</mml:mo> </mml:math> having an important role in summability theory was defined and studied by Maddox (Q. J. Math. 18:345-355, 1967). In the present paper, we generalize the space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>l</mml:mi> <mml:mo>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>)</mml:mo> </mml:math> to the space <mml:math xmlns:mml="http://www...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29962821/boundary-value-problems-for-hypergenic-function-vectors
#7
Guiling Zhang, Chong Li, Yonghong Xie
This article mainly studies the boundary value problems for hypergenic function vectors in Clifford analysis. Firstly, some properties of hypergenic quasi-Cauchy type integrals are discussed. Then, by the Schauder fixed point theorem the existence of the solution to the nonlinear boundary value problem is proved. Finally, using the compression mapping principle the existence and uniqueness of the solution to the linear boundary value problem are proved.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29901025/on-complete-convergence-and-complete-moment-convergence-for-weighted-sums-of-%C3%AF-%C3%A2-mixing-random-variables
#8
Pingyan Chen, Soo Hak Sung
Let <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>r</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>1</mml:mn> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>1</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>p</mml:mi> <mml:mo><</mml:mo> <mml:mn>2</mml:mn> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>β</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:math> with <mml:math xmlns:mml="http://www...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29887726/sharp-bounds-for-the-s%C3%A3-ndor-yang-means-in-terms-of-arithmetic-and-contra-harmonic-means
#9
Hui-Zuo Xu, Yu-Ming Chu, Wei-Mao Qian
In the article, we provide several sharp upper and lower bounds for two Sándor-Yang means in terms of combinations of arithmetic and contra-harmonic means.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29887725/chen-s-ricci-inequalities-and-topological-obstructions-on-null-hypersurfaces-of-a-lorentzian-manifold
#10
Karimumuryango Ménédore
Given a null hypersurface of a Lorentzian manifold, we isometrically immerse a null hypersurface equipped with the Riemannian metric (induced on it by the rigging) into a Riemannian manifold suitably constructed on the Lorentzian manifold. We study the intrinsic and extrinsic geometry of such an isometric immersion and we link them to the null geometry of the null hypersurface in the Lorentzian manifold. In the course of this immersion, we find the basic relationships between the main extrinsic invariants and the main intrinsic invariants, named Chen-Ricci inequalities of the null hypersurface in the Lorentzian manifold...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29881242/extremal-functions-for-trudinger-moser-inequalities-with-nonnegative-weights
#11
Songbo Hou
Using blow-up analysis, the author proves the existence of extremal functions for Trudinger-Moser inequalities with nonnegative weights on bounded Euclidean domains or compact Riemannian surfaces. This extends recent results of Yang (J. Differ. Equ. 258:3161-3193, 2015) and Yang-Zhu (Proc. Am. Math. Soc. 145:3953-3959, 2017).
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29805240/gradient-projection-method-with-a-new-step-size-for-the-split-feasibility-problem
#12
Pattanapong Tianchai
In this paper, we introduce an iterative scheme using the gradient projection method with a new step size, which is not depend on the related matrix inverses and the largest eigenvalue (or the spectral radius of the self-adjoint operator) of the related matrix, based on Moudafi's viscosity approximation method for solving the split feasibility problem (SFP), which is to find a point in a given closed convex subset of a real Hilbert space such that its image under a bounded linear operator belongs to a given closed convex subset of another real Hilbert space...
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29805239/hadamard-and-fej%C3%A3-r-hadamard-inequalities-for-extended-generalized-fractional-integrals-involving-special-functions
#13
Shin Min Kang, Ghulam Farid, Waqas Nazeer, Bushra Tariq
In this paper we prove the Hadamard and the Fejér-Hadamard inequalities for the extended generalized fractional integral operator involving the extended generalized Mittag-Leffler function. The extended generalized Mittag-Leffler function includes many known special functions. We have several such inequalities corresponding to special cases of the extended generalized Mittag-Leffler function. Also there we note the known results that can be obtained.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29805238/optimal-bounds-for-the-generalized-euler-mascheroni-constant
#14
Ti-Ren Huang, Bo-Wen Han, Xiao-Yan Ma, Yu-Ming Chu
We provide several sharp upper and lower bounds for the generalized Euler-Mascheroni constant. As consequences, some previous bounds for the Euler-Mascheroni constant are improved.
2018: Journal of Inequalities and Applications
https://www.readbyqxmd.com/read/29780214/admissibility-of-simultaneous-prediction-for-actual-and-average-values-in-finite-population
#15
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
#16
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
#17
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
#18
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
#19
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
#20
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
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