منابع مشابه
Symmetric Homogeneous Triangle Inequalities
A brief scan through the problem columns of various mathematical journals shows a continual outpouring of proposed problems involving what can be roughly described as “triangle inequalities”. A few examples will suffice to indicate the flavor of these perennial favorites: Let the sides of a triangle be a, b, c and let the angles be A, B, C. Let r and R be the inradius and circumradius, respecti...
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We characterize triples of cevians which form a triangle independent of the triangle where they are constructed. This problem is equivalent to solving a three-parameter family of inequalities which we call Ceva’s triangle inequalities. Our main result provides the parametrization of the solution set. Mathematics subject classification (2010): Primary 26D07, 51M04; secondary 51M15, 15B48.
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We study the reverse triangle inequalities for suprema of logarithmic potentials on compact sets of the plane. This research is motivated by the inequalities for products of supremum norms of polynomials. We find sharp additive constants in the inequalities for potentials, and give applications of our results to the generalized polynomials. We also obtain sharp inequalities for products of norm...
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We present a survey of our recent work on generalized triangle inequalities in infinitesimal symmetric spaces, nonpositively curved symmetric spaces and Euclidean buildings. We also explain how these results can be used to analyze some basic problems of algebraic group theory including the problem of decomposition of tensor products of irreducible representations of complex reductive Lie groups...
متن کاملTriangle inequalities in path metric spaces
We study side-lengths of triangles in path metric spaces. We prove that unless such a space X is bounded, or quasi-isometric to R+ or to R , every triple of real numbers satisfying the strict triangle inequalities, is realized by the side-lengths of a triangle in X . We construct an example of a complete path metric space quasi-isometric to R2 for which every degenerate triangle has one side wh...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2014
ISSN: 1331-4343
DOI: 10.7153/mia-17-44