10,452 Results Found

In the current note, we investigate the mathematical relations among the weighted arithmetic mean–geometric mean (AM–GM) inequality, the Hölder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical...

In this paper, two new refinements of the Erdös–Mordell inequality and three new refinements of Barrow’s inequality are established. Some related interesting conjectures are put forward.

Additive decomposability is an interesting feature of inequality indices which, however, is not always fulfilled; solutions to overcome such an issue have been given by Deutsch and Silber (2007) and by Di Maio and Landoni (2017). In this paper, we ap...

The distance that compares the difference between two probability distributions plays a fundamental role in statistics and machine learning. Optimal transport (OT) theory provides a theoretical framework to study such distances. Recent advances in OT...

This paper derives the sharp bounds for Hermite–Hadamard inequalities in the context of Riemann–Liouville fractional integrals. A generalization of Jensen’s inequality called the Jensen–Mercer inequality is used for general po...

In this article, we delve into the classic Bohr inequality for complex numbers, a fundamental result in complex analysis with broad mathematical applications. We offer refinements and generalizations of Bohr’s inequality, expanding on the estab...

In this work, some numerical radius inequalities based on the recent Dragomir extension of Furuta’s inequality are obtained. Some particular cases are also provided. Among others, the celebrated Kittaneh inequality reads: $w\left(T\right)\le \frac{1}{2}∥\left|T\right|+\left|T^{*}\right|∥$. It is pr...

Society faces challenges in achieving a climate-neutral society due to deepening energy inequality. The pandemic led to reduced emissions but also caused an economic downturn. Geopolitical tensions since 2022 raised energy prices, affecting affordabi...

Accessibility to healthcare services is crucial for residents’ wellbeing. Numerous studies have revealed significant spatial inequality in healthcare accessibility across various contexts. However, it still remains unclear whether the inequalit...

In this paper, we generalize an inequality for a convex function in one dimension ${\mathbb{R}}^1$ on three intervals to a function with nondecreasing increments in k dimensions ${\mathbb{R}}^k$ on $(2n+1)$ intervals. We prove all the situations when $n=1,2$ and prove a very specia...

This paper introduces several refinements of the classical Selberg inequality, which is considered a significant result in the study of the spectral theory of symmetric spaces, a central topic in the field of symmetry studies. By utilizing the contra...

Alongside the economic system reforms and the rapid development of the Chinese economy, wealth gap in China is widening, gradually evolving into an important issue that threatens the sustainable development of China. To comprehensively understand the...

Global material consumption needs to be reduced to be within its planetary boundary. Urbanization and human inequality are two profound economic-social phenomena, which have potential impacts on material consumption. This paper aims to empirically ex...

In this paper, the classical dual mixed volume of star bodies $\tilde{V}(K_1,\cdots ,K_n)$ and dual Aleksandrov–Fenchel inequality are extended to the Orlicz space. Under the framework of dual Orlicz-Brunn-Minkowski theory, we put forward a new affine geo...

The paper explores the changes in the determinants of interprovincial inequality in China during the period of 2000 to 2017 by way of bi-dimensional decomposition method. The method integrates two inequality decompositions by both regional groups and...

Public transport (PT) inequality is evidenced to have adverse consequences on various social–urban–economic aspects of urban residents’ lives; however, the impact of this inequality on PT itself, particularly its utilization, is a l...

The symmetric shape of some inequalities between two sequences of real numbers generates inequalities of the same shape in operator theory. In this paper, we study a new refinement of the Cauchy–Bunyakovsky–Schwarz inequality for Euclidean spaces and...

Following the equivalence between logarithmic Sobolev inequalities and hypercontractivity shown by L. Gross, and applying the ideas and methods of the work by Bobkov, Gentil and Ledoux, we would like to establish a new connection between the logarith...

We investigate the evolution of multidimensional inequality of well-being in Vietnam in the period 2002–2012 using household survey data. Our study focuses on four crucial dimensions of human welfare: consumption, education, health and housing....

In this paper, some vector inequalities for convex maps are proved. The obtained results refer to the famous Jensen inequality and generalize further classical inequalities of Jessen and McShane. In addition, the Hahn–Banach theorems with subli...

Patterns of inequality tend to seriously undermine any attempt at economic growth policy when the inequality is perceived by significant groups of individuals as unjust, inhuman, and insurmountable. One country with a high degree of inequality has be...

In this paper we present some key results related to Blundon’s inequality, its long history, geometric interpretations and implications, as well as highlight some connections to results in other fields of mathematics. We make a case that this i...

We give bounds on the difference between the weighted arithmetic mean and the weighted geometric mean. These imply refined Young inequalities and the reverses of the Young inequality. We also studied some properties on the difference between the weig...

Rising income inequality has become a major concern for policymakers and academic researchers. Very high levels of income inequality may result in serious social, political, and economic problems. In this paper, I analyze the trend of Gini index, whi...

This paper introduces a novel methodology for measuring and decomposing multidimensional inequality, allowing for the breakdown of overall inequality into contributions from distinct dimensions. This approach offers valuable insights for sustainable...

To achieve a balanced and sustainable rural development pattern, this study used the Theil index, Gini coefficient, and Spatial Autocorrelation method to analyze the inequality of industrial economic development between rural areas in South Korea. Th...

In diverse branches of mathematics, several inequalities have been studied and applied. In this article, we improve Furuta’s inequality. Subsequently, we apply this improvement to obtain new radius inequalities that not been reported in the cur...

Increasing economic inequality in recent years has triggered an outpouring of analysis and reflection on the causes and consequences of these changes. Several commentators have argued that inequality does not merit all the attention it has been recei...

We focus on the improvement of operator Kantorovich type inequalities. Among the consequences, we improve the main result of the paper [H.R. Moradi, I.H. Gümüş, Z. Heydarbeygi, A glimpse at the operator Kantorovich inequality, Linear Multil...

Land related inequality is a central component of the wider inequality that is one of the burning issues of our society today. It affects us all and directly determines the quality of life for billions of people who depend on land and related resourc...

Let $p,q\ge 1$ be two real numbers such that ${\displaystyle \frac{1}{p}}+{\displaystyle \frac{1}{q}}=1$, and let $a,b\in \mathbb{R}$ be two parameters defined on the domain of a function, for example, f. Based on the well known Hölder inequality, we propose a generic inequality of the form $\left|f({\displaystyle \frac{a}{p}}+{\displaystyle \frac{b}{q}})\right|\le |f$...

Understanding the spatial or geographical dependence of income inequality and regional inequality is crucial in the study of inequality. This paper employs a multi-scale, multi-mechanism framework to map and analyze historical patterns of regional an...

In this paper, we proved a weighted Hardy–Rellich inequality for Dunkl operators based on the spherical h-harmonic decomposition theory of Dunkl operators. Moreover, we obtained the explicit constant of the inequalities, which is optimal in som...

We obtain a Rellich type inequality on the sphere and give the corresponding best constant. The result complements some related inequalities in recent literatures.

Within the recent wave of research advancements, mathematical inequalities and their practical applications play a notably significant role across various domains. In this regard, inequalities offer a captivating arena for scholarly endeavors and inv...

Extreme inequality represents a grave challenge for impoverished individuals and poses a threat to economic growth and stability. Despite the fulfillment of affirmative action measures aimed at promoting equal opportunities, they often prove inadequa...

Inequality indices are quantitative scores that take values in the unit interval, with a zero score denoting complete equality. They were originally created to measure the heterogeneity of wealth metrics. In this study, we focus on a new inequality i...

In this paper we provide many new results involving Opial type inequalities. We consider two functions—one is convex and the other is concave—and prove a new general inequality on a measure space $(\mathsf{\Omega },\mathsf{\Sigma },\mu )$. We give an new res...

International law in general, and international economic law in particular, to the extent that either has focused on the issue of inequality, has done so in terms of inequality between states. Largely overlooked has been the topic of inequality withi...

Reducing global greenhouse gas emissions and implementing sustainable environmental policies require the identification of the economic, political, ecological, and social factors that affect emission levels. To this end, this study examines, for the...

The primary goal of this research is to prove some new Hardy-type ∇-conformable dynamic inequalities by employing product rule, integration by parts, chain rule and $(\gamma ,a)$-nabla Hölder inequality on time scales. The inequalities proved here extend and...

On the presumption that poorer people tend to work less, it is often claimed that standard measures of inequality and poverty are overestimates. The paper points to a number of reasons to question this claim. It is shown that, while the labor supplie...

Recent research on the effects of the productive structure of an economy has turned to examining whether economic complexity is associated with lower income inequality. In contrast to the commonly adopted approach that estimates the impact of economi...

This study investigates the relationship between stock returns and income inequality in South Africa, a country marked by persistently high levels of income disparities and a sophisticated and structurally unique financial market. Despite the Johanne...

Aggregation operators have become an essential tool in many applications. The functional equations related to aggregation operators play an important role in fuzzy sets and fuzzy logic theory. The modular equation is strongly connected with the distr...

Economic inequality at the local level has been shown to be an important predictor of people’s political perceptions and preferences. However, research on these questions is hampered by the fact that local inequality is difficult to measure and syste...

We investigate the distillability problem in quantum information in ${ℂ}^d\otimes {ℂ}^d$ . One case of the problem has been reduced to proving a matrix inequality when $d=4$ . We investigate the inequality for three families of non-norm...

Child health has been addressed as a priority at both global and national levels for many decades. In China, difficulty of accessing paediatricians has been of debate for a long time, however, there is limited evidence to assess the population- and g...

The level of world urbanization has crossed the 50% mark, and nearly all future population growth is projected to occur in cities. Cities are disproportionately wealthy, but are associated with poverty, too. Addressing the dual challenges of urbaniza...

The primary focus of this paper is on the relationship between taxpayers’ ideological support for economic inequality and the likelihood they will commit tax evasion. We also propose that Machiavellianism will mediate the relationship between s...