General Inequality Research Articles

Eigenvalue inequalities for the buckling problem of the drifting Laplacian of arbitrary order

Abstract In this paper, we investigate the buckling problem of the drifting Laplacian of arbitrary order on a bounded connected domain in complete smooth metric measure spaces (SMMSs) supporting a special function, and successfully obtain a general inequality for its eigenvalues. By applying this general inequality, if the complete SMMSs considered satisfy some curvature constraints, we can obtain a universal inequalities for eigenvalues of this buckling problem.

Some General Fractional Integral Inequalities Involving LR–Bi-Convex Fuzzy Interval-Valued Functions

The main objective of this paper is to introduce a new class of convexity called left-right–bi-convex fuzzy interval-valued functions. We study this class from the perspective of fractional Hermite–Hadamard inequalities, involving a new fractional integral called the left-right–AB fractional integral. We discuss several special cases that demonstrate that our results are quite unifying. We provide non-trivial numerical examples regarding special means for positive real numbers in order to check the validity of our outcomes.

Generalization of Some Integral Inequalities for Arithmetic Harmonically Convex Functions

In this study, by using an integral identity, Hölder integral inequality and modulus properties we obtain some new general inequalities of the Hermite-Hadamard and Bullen type for functions whose derivatives in absolute value at certain power are arithmetically harmonically (AH) convex. In the last part of the article, applications including arithmetic mean, geometric mean, harmonic mean, logarithmic mean and p-logarithmic mean, which are some special means of real numbers, are given by using arithmetic harmonically convex functions.

Iterative algorithms for general variational inequalities involving relaxed Lipschitz operators

In this paper, we establish and discuss the existence of a solution of the general variational inequality : Find u ∈ H, and ω ∈ T(u) such that h(u) ∈ K and This variational inequality was studied by Verma [3] in case s ≡ 0, and g ≡ I.

Robust convex optimization: A new perspective that unifies and extends

Robust convex constraints are difficult to handle, since finding the worst-case scenario is equivalent to maximizing a convex function. In this paper, we propose a new approach to deal with such constraints that unifies most approaches known in the literature and extends them in a significant way. The extension is either obtaining better solutions than the ones proposed in the literature, or obtaining solutions for classes of problems unaddressed by previous approaches. Our solution is based on an extension of the Reformulation-Linearization-Technique, and can be applied to general convex inequalities and general convex uncertainty sets. It generates a sequence of conservative approximations which can be used to obtain both upper- and lower- bounds for the optimal objective value. We illustrate the numerical benefit of our approach on a robust control and robust geometric optimization example.

A primal-dual interior-point relaxation method with global and rapidly local convergence for nonlinear programs

Based on solving an equivalent parametric equality constrained mini-max problem of the classic logarithmic-barrier subproblem, we present a novel primal-dual interior-point relaxation method for nonlinear programs with general equality and nonnegative constraints. In each iteration, our method approximately solves the KKT system of a parametric equality constrained mini-max subproblem, which avoids the requirement that any primal or dual iterate is an interior-point. The method has some similarities to the warmstarting interior-point methods in relaxing the interior-point requirement and is easily extended for solving problems with general inequality constraints. In particular, it has the potential to circumvent the jamming difficulty that appears with many interior-point methods for nonlinear programs and improve the ill conditioning of existing primal-dual interior-point methods as the barrier parameter is small. A new smoothing approach is introduced to develop our relaxation method and promote convergence of the method. Under suitable conditions, it is proved that our method can be globally convergent and locally quadratically convergent to the KKT point of the original problem. The preliminary numerical results on a well-posed problem for which many interior-point methods fail to find the minimizer and a set of test problems from the CUTEr collection show that our method is efficient.

A visual proof that b a < a b when e ≤ a < b

In a recent Mathematical Intelligencer note, B. Chakraborty [A visual proof that π e < e π . Mathematical Intelligencer, 41(1), 56] provided a visual proof of the inequality π e < e π . The aim of this classroom capsule is to visualize the more general inequality b a < a b , where e ≤ a < b in an amazing way.

Improved Stability Criteria for Delayed Neural Networks via a Relaxed Delay-Product-Type Lapunov–Krasovskii Functional

In this paper, the asymptotic stability problem of neural networks with time-varying delays is investigated. First, a new sufficient and necessary condition on a general polynomial inequality was developed. Then, a novel augmented Lyapunov–Krasovskii functional (LKF) was constructed, which efficiently introduces some new terms related to the previous information of neuron activation function. Furthermore, based on the suitable LKF and the stated negative condition of the general polynomial, two criteria with less conservatism were derived in the form of linear matrix inequalities. Finally, two numerical examples were carried out to confirm the superiority of the proposed criteria, and a larger allowable upper bound of delays was achieved.

Nonlocal Harnack inequalities in the Heisenberg group

We deal with a wide class of nonlinear integro-differential problems in the Heisenberg-Weyl group mathbb {H}^n, whose prototype is the Dirichlet problem for the p-fractional subLaplace equation. These problems arise in many different contexts in quantum mechanics, in ferromagnetic analysis, in phase transition problems, in image segmentations models, and so on, when non-Euclidean geometry frameworks and nonlocal long-range interactions do naturally occur. We prove general Harnack inequalities for the related weak solutions. Also, in the case when the growth exponent is p=2, we investigate the asymptotic behavior of the fractional subLaplacian operator, and the robustness of the aforementioned Harnack estimates as the differentiability exponent s goes to 1.

A Unified Inertial Iterative Approach for General Quasi Variational Inequality with Application

In this paper, we design two inertial iterative methods involving one and two inertial steps for investigating a general quasi-variational inequality in a real Hilbert space. We establish an existence result and a non-trivial example is furnished to substantiate our theoretical findings. We discuss the convergence of the inertial iterative algorithms to approximate the solution of a general quasi-variational inequality. Finally, we apply an inertial iterative scheme with two inertial steps to investigate a delay differential equation. The results presented herein can be seen as substantial generalizations of some known results.

Potential energy of totally positive algebraic integers

Given positive real numbers, we prove two inequalities involving their potential energy and their power sums. We also prove a general inequality involving the energy and the discriminant. This can be applied to the case of totally positive irreducible polynomials, although in that more specialised setting the results are weaker than those obtained by Smyth's method.

Łoskot-Rudnicki’s Inequality and General Relative Entropy Inequality for Cauchy Problems Preserving Positivity

The Generalized Relative Entropy inequality is a ubiquitous property in mathematical models applied in physics or biology. In spite of its importance, it is currently proved on a case-by-case basis in the literature. Here, we show that GRE is actually a generic consequence of Łoskot-Rudnicki’s inequality that is reminiscent of Jensen’s inequality.

The Impact of Different Levels of Income Inequality on Subjective Well-Being in China: A Panel Data Analysis

Income inequality is one of the most serious issues globally and China is the representative examples of this issue. Income inequality remains high in China and may negatively affects subjective well-being. This study clarifies whether income inequality affects subjective well-being in China. Using five waves of the 2010-2018 data from China Family Panel Studies, a panel data analysis reveals the following: First, general income inequality measured by provincial Gini coefficients has a significant U-shaped impact. Second, between-group income inequality, measured as income ratio between urban hukou residents and migrants with rural hukou, has a significant U-shaped impact. Third, urban-rural income inequality measured by provincial urban to rural household per capita income ratio has an inverted-U-shaped impact. To address endogeneity problems of income inequality, this study adopts instrumental variable approach. For the further robustness checks of the validity of the instrumental variable used, this study adopts the recent Conley et al. (2012) bounds approach. Our results are robust after addressing endogeneity problem. One important policy implication stemming from our results is the need to adopt strategies that ensure a more inclusive society without hukou-related and urban–rural discrimination.

Who suffers from COVID-19 shock? Labour market risk and wage inequality in China

ABSTRACT Through an online survey from 2020, this study aims to investigate how labour market status and occupational factors shape the risk of wage drops resultant of the COVID-19 outbreak. Quantitative evidence shows the risk is amplified for lower-educated labourers working in administrative positions, and affiliated to the traditional service sector and foreign invested enterprises (FIE) and they are more likely to experience earning reduction. COVID-19 in China witnesses a significantly downward trend of labours` wage and general wage inequality has slightly eased. This study calls for policy shift in direct financial subsidies to workers to mitigate labours’ risk.

A general minimax inequality and its consequences

A general minimax inequality and its consequences

Strengthened Fractional Sobolev Type Inequalities in Besov Spaces

The purpose of this article is twofold. The first is to strengthen fractional Sobolev type inequalities in Besov spaces via the classical Lorentz space. In doing so, we show that the Sobolev inequality in Besov spaces is equivalent to the fractional Hardy inequality and the iso-capacitary type inequality. Secondly, we will strengthen fractional Sobolev type inequalities in Besov spaces via capacitary Lorentz spaces associated with Besov capacities. For this purpose, we first study the embedding of the associated capacitary Lorentz space to the classical Lorentz space. Then, the embedding of the Besov space to the capacitary Lorentz space is established. Meanwhile, we show that these embeddings are closely related to the iso-capacitary type inequalities in terms of a new-introduced fractional (β,p,q)-perimeter. Moreover, characterizations of more general Sobolev type inequalities in Besov spaces have also been established.

Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals

Our aim in this paper is to establish new $\eta -$conformable fractional integral. For this purpose new inequalities are obtained by using generalized $\eta -$conformable fractional integral with the help of Grüss type integrals. The inequalities that exist in the literature are obtained in case of some special choices, which shows that the inequality we achieve is a more general inequality.

An inexact operator splitting method for general mixed variational inequalities

The present paper aims to deal with an inexact implicit method with a variable parameter for generalmixed variational inequalities in the setting of real Hilbert spaces. Under standard assumptions, the globalconvergence of the proposed method is proved. Numerical example is presented to illustrate the proposedmethod and convergence result. The results and method presented in this paper generalize, extend and unifysome known results in the literature.

The Role of Circumstances in The Differentiation of Russian Wages

The purpose of this study is to determine the influence of circumstances (opportunities) and efforts on the wages differentiation of Russian citizens. Research objectives: identification of factors of circumstances, quantitative assessment of their contribution to the wages of Russians and their individual income groups. The research is based on the HSE RLMS data for 2004 and 2018 and LITS-III data for 2016. We applied parametric methods of regression analysis, the Morduch-Sicular method of inequality decomposition, as well as the construction of quantile regressions. As a result of the study, we obtained assessments of the contribution of circumstances to wages inequality of the Russian population. We found that income inequality in the Russian labour market was primarily determined by the regional factor, to a lesser extent by the employment sector and the gender of the respondents. The least contribution to inequality was made by the factor of the employment formality. The influence of parents’ education on future earnings of offspring was also negligible – according to the model based on the LITS-III sample. The reduction in the contribution of circumstances to the general wage inequality in Russia in 2004–2018 was mainly due to a decrease in interregional differences in wages, where an active government policy of income redistribution played a significant role. The influence of circumstances on wage inequality was uneven in different quantiles of the distribution scale. In particular, employment in the metropolitan area or in the oil and gas sector has been most beneficial to high-income groups of workers. At the same time, parents’ education had the least and even negative effect on the earnings of the highest-paid people, which can be explained by the peculiarities of the formation of the modern Russian elite. The results of the study are applicable for conducting an effective social policy of the state.

Several Double Inequalities for Integer Powers of the Sinc and Sinhc Functions with Applications to the Neuman–Sándor Mean and the First Seiffert Mean

In the paper, the authors establish a general inequality for the hyperbolic functions, extend the newly-established inequality to trigonometric functions, obtain some new inequalities involving the inverse sine and inverse hyperbolic sine functions, and apply these inequalities to the Neuman–Sándor mean and the first Seiffert mean.