Search results for "Equality"
showing 10 items of 1338 documents
Improvement of Grüss and Ostrowski type inequalities
2015
Several inequalities of Ostrowski-Gr?ss-type available in the literature are generalized considering the weighted case of them. The inequality of Gr?ss type proved by P. Cerone and S.S. Dragomir [3] is extended for the weighted case.
A note on multiple summing operators and applications
2018
We prove a new result on multiple summing operators and, among other results and applications, we provide a new extension of Littlewood’s 4 / 3 inequality to m-linear forms.
Vectors and Vector Fields
2012
The purpose of this book is to explain in a rigorous way Stokes’s theorem and to facilitate the student’s use of this theorem in applications. Neither of these aims can be achieved without first agreeing on the notation and necessary background concepts of vector calculus, and therein lies the motivation for our introductory chapter.
Understanding trends and drivers of urban poverty in American cities
2022
Urban poverty arises from the uneven distribution of poor populations across neighborhoods of a city. We study the trend and drivers of urban poverty across American cities over the last 40 years. To do so, we resort to a family of urban poverty indices that account for features of incidence, distribution, and segregation of poverty across census tracts. Compared to the universally-adopted concentrated poverty index, these measures have a solid normative background. We use tract-level data to assess the extent to which demographics, housing, education, employment, and income distribution affect levels and changes in urban poverty. A decomposition study allows to single out the effect of cha…
APOE epsilon variation in multiple sclerosis susceptibility and disease severity: some answers
2006
Background: Previous studies have examined the role of APOE variation in multiple sclerosis (MS), but have lacked the statistical power to detect modest genetic influences on risk and disease severity. The meta- and pooled analyses presented here utilize the largest collection, to date, of MS cases, controls, and families genotyped for the APOE epsilon polymorphism. Methods: Studies of MS and APOE were identified by searches of PubMed, Biosis, Web of Science, Cochrane Review, and Embase. When possible, authors were contacted for individual genotype data. Meta-analyses of MS case-control data and family-based analyses were performed to assess the association of APOE epsilon genotype with dis…
Best approximation and variational inequality problems involving a simulation function
2016
We prove the existence of a g-best proximity point for a pair of mappings, by using suitable hypotheses on a metric space. Moreover, we establish some convergence results for a variational inequality problem, by using the variational characterization of metric projections in a real Hilbert space. Our results are applicable to classical problems of optimization theory.
Hölder stability for Serrin’s overdetermined problem
2015
In a bounded domain \(\varOmega \), we consider a positive solution of the problem \(\Delta u+f(u)=0\) in \(\varOmega \), \(u=0\) on \(\partial \varOmega \), where \(f:\mathbb {R}\rightarrow \mathbb {R}\) is a locally Lipschitz continuous function. Under sufficient conditions on \(\varOmega \) (for instance, if \(\varOmega \) is convex), we show that \(\partial \varOmega \) is contained in a spherical annulus of radii \(r_i 0\) and \(\tau \in (0,1]\). Here, \([u_\nu ]_{\partial \varOmega }\) is the Lipschitz seminorm on \(\partial \varOmega \) of the normal derivative of u. This result improves to Holder stability the logarithmic estimate obtained in Aftalion et al. (Adv Differ Equ 4:907–93…
Thin obstacle problem : Estimates of the distance to the exact solution
2018
We consider elliptic variational inequalities generated by obstacle type problems with thin obstacles. For this class of problems, we deduce estimates of the distance (measured in terms of the natural energy norm) between the exact solution and any function that satisfies the boundary condition and is admissible with respect to the obstacle condition (i.e., they are valid for any approximation regardless of the method by which it was found). Computation of the estimates does not require knowledge of the exact solution and uses only the problem data and an approximation. The estimates provide guaranteed upper bounds of the error (error majorants) and vanish if and only if the approximation c…
Isoperimetric inequality via Lipschitz regularity of Cheeger-harmonic functions
2014
Abstract Let ( X , d , μ ) be a complete, locally doubling metric measure space that supports a local weak L 2 -Poincare inequality. We show that optimal gradient estimates for Cheeger-harmonic functions imply local isoperimetric inequalities.