Class Of Inequalities Research Articles

Some Refinements and Generalizations of Bohr’s Inequality

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 established inequalities of N. G. de Bruijn and Radon, as well as leveraging the class of functions defined by the Daykin–Eliezer–Carlitz inequality. Our novel contribution lies in demonstrating that Bohr’s and Bergström’s inequalities can be derived from one another, revealing a deeper interconnectedness between these results. Furthermore, we present several new generalizations of Bohr’s inequality, along with other notable inequalities from the literature, and discuss their various implications. By providing more comprehensive and verifiable conditions, our work extends previous research and enhances the understanding and applicability of Bohr’s inequality in mathematical studies.

Some New Approaches to Fractional Euler–Maclaurin-Type Inequalities via Various Function Classes

This paper aims to examine an approach that studies many Euler–Maclaurin-type inequalities for various function classes applying Riemann–Liouville fractional integrals. Afterwards, our results are provided by using special cases of obtained theorems and examples. Moreover, several Euler–Maclaurin-type inequalities are presented for bounded functions by fractional integrals. Some fractional Euler–Maclaurin-type inequalities are established for Lipschitzian functions. Finally, several Euler–Maclaurin-type inequalities are constructed by fractional integrals of bounded variation.

Sumset Estimates in Convex Geometry

Abstract Sumset estimates, which provide bounds on the cardinality of sumsets of finite sets in a group, form an essential part of the toolkit of additive combinatorics. In recent years, probabilistic or entropic forms of many of these inequalities were introduced. We study analogues of these sumset estimates in the context of convex geometry and the Lebesgue measure on ${\mathbb{R}}^{n}$. First, we observe that, with respect to Minkowski summation, volume is supermodular to arbitrary order on the space of convex bodies. Second, we explore sharp constants in the convex geometry analogues of variants of the Plünnecke-Ruzsa inequalities. In the last section of the paper, we provide connections of these inequalities to the classical Rogers-Shephard inequality.

An Ecofeminist Contribution to the Debates on the Neoextractivist Development Model in Latin America

This article presents a materialist ecofeminist critique of neoextractivism by highlighting its historical origins and elaborating its economic policy implications in Latin America. Three questions addressed are as follows: 1) How can materialist ecofeminism contribute to understanding the current dynamics of capitalist development in the Global South, 2) why (neo)extractivism hits women hardest, and 3) to what extent and how ecofeminist movements can shape a post-extractivist transition to a just and sustainable future. The article’s main argument is that exploitation and oppression in Latin America can be understood in terms of gender, race, and class and, therefore, require an intersectional analysis framework. Within this framework, post-extractivist alternatives in this region must incorporate an ecofeminist analysis to understand better how social expression systems (including sexism, white supremacy, and ecological crises) intersect and reinforce each other. In this framework, this study is intended to contribute to the growing literature and debate on the development and resistance dynamics of neoextractivism in Latin America, where long-standing racial and gender inequalities intersect with class inequalities.

Upward Mobility and Class Inequities among Filipino Migrant Nurses in the Republic of Ireland

Upward Mobility and Class Inequities among Filipino Migrant Nurses in the Republic of Ireland

Weak monotonicity property of Korevaar-Schoen norms on nested fractals

In this paper, we study the weak monotonicity property of Korevaar-Schoen (p-energy) norms on nested fractals for 1<p<∞. Such property has many important applications on fractals and other metric measure spaces, such as constructing p-energies (when p=2 this is basically a Dirichlet form), generalizing the classical Sobolev type inequalities and the celebrated Bourgain-Brezis-Mironescu convergence.

Fractional Euler-Maclaurin-type inequalities for various function classes

This paper investigates a technique that uses Riemann-Liouville fractional integrals to study several Euler-Maclaurin-type inequalities for various function classes. Afterwards, we provide our results by using special cases of obtained theorems and This paper is to derive examples. Moreover, we give some Euler-Maclaurin-type inequalities for bounded functions by fractional integrals. Furthermore, we construct some fractional Euler-Maclaurin-type inequalities for Lipschitzian functions. Finally, we offer some Euler-Maclaurin-type inequalities by fractional integrals of bounded variation.

Transport-entropy and functional forms of Blaschke–Santaló inequalities

We explore alternative functional or transport-entropy formulations of the Blaschke–Santaló inequality. In particular, we obtain new Blaschke–Santaló inequalities for s -concave functions. We also obtain new sharp symmetrized transport-entropy inequalities for a large class of spherically invariant probability measures, including the uniform measure on the unit Euclidean sphere and generalized Cauchy and Barenblatt distributions.

The View from Above and Below: Subjective Mobility and Explanations of Class, Race, and Gender Inequality

Abstract Popular explanations of inequality as the result of individual failings rather than structural processes are powerful cultural mechanisms that legitimize and reproduce inequality in the United States. How might individuals’ experiences of downward or upward mobility shape the explanations they give? We argue that perceived experiences of economic mobility may not only shape how Americans understand economic inequality but may also impact their beliefs about social inequalities more broadly. Using proportionally representative survey data of 1110 U.S. residents, we find that those who perceive that they currently occupy a lower economic class than when they were growing up (i.e., they experienced subjective downward mobility) were more likely than class-stable individuals to reject individualistic explanations of economic inequality and embrace structural ones. By contrast, the upwardly mobile were more likely to reject structural explanations. We find that mobility is similarly related to the likelihood of giving individualistic or structural explanations for race and gender inequality as well. Downward mobility is also associated with greater support of redistributive policies related to economic as well as gender and race inequality. These findings suggest that economic mobility may influence popular explanations of inequality and support for redistributive policy not only related to class inequality but for multiple axes of inequality.

“Why Is the Old Dying and the New Is Not Being Born?” The Church’s Struggle with Public Justice and Righteousness in Zimbabwe

Abstract This article attempts to present how the church has struggled with public justice and righteousness in Zimbabwe where the past and old dominate the national debate without giving room for emerging personalities and ideas. The church introduced programmes, organisations and documents in an attempt to theoretically break away with the past. The documents are results of transformative projects designed to address the holistic needs of people in Zimbabwe against both the localised and internationalised neoliberal paradigms of Capitalism, Colonialism and Christianity that disempowered rather than liberated followers. Being critical of the past, Derrida says: “To ask such questions, such difficult questions, requires that we change the most resistant, archaic structures of our desire”. The Zimbabwe Heads of Christian Denominations (ZHOCD s) introduced the post-liberation discourse through the Zimbabwe We Want Document (ZWWD) in 2006, and a national economic discussion through the National Holistic Agenda for Renewal and Empowerment (NHARE) in 2019 against the idea that the Church must be confined in the pews and politicians in the public arena. These documents and programmes engaged with both politicians and citizens in critical ways to achieve both justice and righteousness. Justice and righteousness are big themes in the Bible and Christian doctrine. Breaking away with the past promised to reverse the slippery slope on public life in Zimbabwe that increased national poverty, class inequalities, and factionalised politics. The opening of space in public life by the ZHOCD allowed citizens to engage in all public life and justice struggles, which is “a revival of a voice that has been silenced after independence, or was send to the Intensive Care Unit (ICU), paralysed, captured, neutralised or unauthorised”. It explored new alternatives to engaging state theology in relationship to the margins. Scripture has been useful in the church’s engagement with the state on public life goods, hence the question: “Why is the old dying and the new not being born”? The article pursues this question in view of the church programmes and documents.

The Balancing Act of Family and College: Reciprocity and Its Consequences for Black Students

Abstract Literature indicates the ways that young adults –especially those from advantaged backgrounds—rely on parents during college and the transition to adulthood. Little research focuses on how the Black family reaches into college and Black college students’ provision of support to parents and other kin. The nexus of family and higher education is a rich site for investigating inequalities in educational attainment and outcomes. Based on interviews with Black undergraduates, this paper analyzes variation in familial involvement during college. It shows the ways in which Black students maintain a balancing act to meet academic responsibilities and family obligations. These practices help sustain the families they value but also reproduce class inequalities. The social organization of colleges and families imposes greater costs on disadvantaged students and offers greater benefits for advantaged students. The structure of education and constructions of family diminish obligations to family, narrow family ties, and mystify aspects of dependence, especially for disadvantaged students. Student narratives highlight the broad character of family values that often compete with academic obligations and detract from college immersion. Different forms and patterns of assistance and connection by class and gender are tied to structural resources and cultural differences, such as the place of family, the meaning of self, assessments of who counts as family, and reliance on a norm of one-way giving.

New refinements of some classical inequalities via Young’s inequality

New refinements of some classical inequalities via Young’s inequality

A version of the Hermite-Hadamard inequality for Quasi F−(h,g,m)-convex functions

This paper aims to present Hermite-Hadamard type inequalities for a new class of functions, which will be denoted by Q h , g m ( F ; I ) an and called class of quasi F − ( h , g ; m ) -convex functions defined on interval I . Many well known classes of functions can be recaptured from this new quasi convexity in particular cases. Also, several publish results are obtained along with new kinds of inequalities.

Tri-composed fuzzy relation inequality with weighted-max-min composition and the relevant min-max optimization problem

In the existing works, the classical fuzzy relation inequality (FRI) with double-composed operators has been introduced to describe the P2P network system. In this work, considering the successful rate of the line connection within the P2P network system, we establish the so-called tri-composed FRI, with a weighted-max-min composition, for the first time. We study the solutions induced through paths and further construct the complete solution set of the tri-composed FRI using the path-induced solutions. Moreover, the whole solution set could be fully determined by all the path-induced solutions and its unique maximum solution. Furthermore, considering a specific optimal management objective in the P2P network, we further study the min-max optimization problem with the tri-composed FRI constraints. A path-based algorithm is proposed for handling the problem we studied, accompanied by an illustrative example.

Chebyshev–Jensen-Type Inequalities Involving χ-Products and Their Applications in Probability Theory

By means of the functional analysis theory, reorder method, mathematical induction and the dimension reduction method, the Chebyshev-Jensen-type inequalities involving the χ-products ⟨·⟩χ and [·]χ are established, and we proved that our main results are the generalizations of the classical Chebyshev inequalities. As applications in probability theory, the discrete with continuous probability inequalities are obtained.

Second-order moments of the size of randomly induced subgraphs of given order

For a graph G and a positive integer c, let Mc(G) be the size of a subgraph of G induced by a randomly sampled subset of c vertices. Second-order moments of Mc(G) encode part of the structure of G. We use this fact, coupled to classical moment inequalities, to prove graph theoretical results, to give combinatorial identities, to bound the size of the c-densest subgraph from below and the size of the c-sparsest subgraph from above, and to provide bounds for approximate enumeration of trivial subgraphs.

On some operator norm inequalities

In this paper, we use known classical inequalities to establish some operator norm inequalities for a pair of norm-attainable operators on a complex Hilbert space.

Operator Bohr-type inequalities

Abstract The classical Bohr inequality for scalars was extended to the non-commutative case of Hilbert space operators in the literature. The sole goal of this article is to discuss the operator Bohr inequality and present some of its new variants. This includes fresh reverses and refinements of this inequality with applications towards an operator’s real and imaginary parts, not to forget the new discussion of different domains of the parameters. One further application towards the operator Dunkl-Williams inequality will be presented too. While the new results are interesting, we emphasize that the approach used to explore these inequalities differs from the existing literature methods for this context.

On the hyper-Lyapunov matrix inclusions

By adding a scalar parameter to the classical Lyapunov matrix inequality, the underlying structure turns to be richer: Partial order of stability sets is introduced. This is then used to improve estimates of trajectories associated with differential inclusions.Technically, the spectrum of all matrices, satisfying a given Lyapunov inequality, lies within a special disk in the right-half plane: Under inversion such a disk is mapped onto itself.As a by-product, it is shown that these disks are a natural tool to understanding the Matrix-Sign-Function iteration scheme, used in matrix computations.Hyper-Lyapunov inclusions are formulated through Matrix-Quadratic-Form Inequalities and so are the analogous Hyper-Stein sets of matrices whose spectrum lies within sub-unit disks.

How are romantic cross-class relationships sustained?

How are romantic relationships across class maintained under broader conditions of class inequality? This article draws on in-depth interviews with 38 people who have partnered across class in Australia. It examines the emotional and interpersonal labour required to preserve such relationships within a highly differentiated class structure that is widely obscured in public and political life. We find, first, that for people in committed cross-class relationships where this difference was openly acknowledged, class difference was acutely felt and described in highly emotional, imprecise terms. Second, this heightened awareness of class difference stimulated elevated levels of class friction and class dissonance within these relationships. We detail these experiences, as they were narrated to us, before examining certain interviewees' efforts to understand and resolve these complexities. We highlight the collaborative work undertaken by one couple in particular to navigate feelings of class discomfort and class dissonance. Third, by focussing on the emotional terrain of intimate cross-class negotiations, we stress moments which have the potential to disrupt assumptions about class hierarchies and modes of moral distinction that take place within these relationships. Proceeding to tentatively valorise different forms of value-making and recognition within cross-class relationships, we also pay attention to the role of class in enabling this very capacity for adaptation.