منابع مشابه
Convex Sets and Inequalities
Given a natural correspondence between a family of inequalities and a closed convex set in a topological linear space, one might expect that an inequality corresponding to a special point (e.g., an extreme point) would be of special interest in view of the convex analysis theory. In this paper, we realize this concept. Let X be an arbitrary set and {φ0,φ1,φ} a triple of nonnegative real-valued ...
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Variational inequalities and even quasi-variational inequalities, as means of expressing constrained equilibrium, have utilized geometric properties of convex sets, but the theory of tangent cones and normal cones has yet to be fully exploited. Much progress has been made in that theory in recent years in understanding the variational geometry of nonconvex as well as convex sets and applying it...
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Every convex set in the plane gives rise to geometric functionals such as the area, perimeter, diameter, width, inradius and circumradius. In this paper, we prove new inequalities involving these geometric functionals for planar convex sets containing zero or one interior lattice point. We also conjecture two results concerning sets containing one interior lattice point. Finally, we summarize k...
متن کاملTurán type reverse Markov inequalities for compact convex sets
For a compact convex set K ⊂ C the well-known general Markov inequality holds asserting that a polynomial p of degree n must have ∥∥p′∥∥ c(K)n2 ‖p‖. On the other hand for polynomials in general, ∥∥p′∥∥ can be arbitrarily small as compared to ‖p‖. The situation changes when we assume that the polynomials in question have all their zeroes in the convex set K. This was first investigated by Turán,...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2005
ISSN: 1029-242X
DOI: 10.1155/jia.2005.107