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On the triangle inequality in normed spaces
"... The triangle inequality is undoubtedly one of the most fundamental inequalities in mathematics. Let X be a normed (Banach) space. For any vectors x, y ∈ X, x+ y  ≤ x+ y  (Triangle inequality). ..."
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The triangle inequality is undoubtedly one of the most fundamental inequalities in mathematics. Let X be a normed (Banach) space. For any vectors x, y ∈ X, x+ y  ≤ x+ y  (Triangle inequality).
Generalizations of the triangle inequality
 Department of Mathematics, Ferdowsi University
"... ABSTRACT. The triangle inequality ‖x + y ‖ ≤ (‖x ‖ + ‖y‖) is wellknown and fundamental. Since the 8th General Inequalities meeting in Hungary (September 1521, 2002), the author has been considering an idea that as triangle inequality, the inequality ‖x + y ‖ 2 ≤ 2(‖x ‖ 2 + ‖y ‖ 2) may be more sui ..."
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Cited by 6 (1 self)
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ABSTRACT. The triangle inequality ‖x + y ‖ ≤ (‖x ‖ + ‖y‖) is wellknown and fundamental. Since the 8th General Inequalities meeting in Hungary (September 1521, 2002), the author has been considering an idea that as triangle inequality, the inequality ‖x + y ‖ 2 ≤ 2(‖x ‖ 2 + ‖y ‖ 2) may be more
Ceva’s triangle inequalities
"... Abstract. We characterize triples of cevians which form a triangle independent of the triangle where they are constructed. This problem is equivalent to solving a threeparameter family of inequalities which we call Ceva’s triangle inequalities. Our main result provides the parametrization of the so ..."
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Abstract. We characterize triples of cevians which form a triangle independent of the triangle where they are constructed. This problem is equivalent to solving a threeparameter family of inequalities which we call Ceva’s triangle inequalities. Our main result provides the parametrization
Bregman Divergences and Triangle Inequality
"... While Bregman divergences have been used for clustering and embedding problems in recent years, the facts that they are asymmetric and do not satisfy triangle inequality have been a major concern. In this paper, we investigate the relationship between two families of symmetrized Bregman divergences ..."
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While Bregman divergences have been used for clustering and embedding problems in recent years, the facts that they are asymmetric and do not satisfy triangle inequality have been a major concern. In this paper, we investigate the relationship between two families of symmetrized Bregman divergences
Concept dissimilarity with triangle inequality
 in KR’14
, 2014
"... Several researchers have developed properties that ensure compatibility of a concept similarity or dissimilarity measure with the formal semantics of Description Logics. While these authors have highlighted the relevance of the triangle inequality, none of their proposed dissimilarity measures sa ..."
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Cited by 1 (1 self)
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Several researchers have developed properties that ensure compatibility of a concept similarity or dissimilarity measure with the formal semantics of Description Logics. While these authors have highlighted the relevance of the triangle inequality, none of their proposed dissimilarity measures
Reverse Triangle Inequalities for Potentials
"... Dedicated to George G. Lorentz, whose works have been a great inspiration Abstract. 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 sha ..."
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Cited by 3 (1 self)
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Dedicated to George G. Lorentz, whose works have been a great inspiration Abstract. 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
ON THE TRIANGLE INEQUALITY IN QUASIBANACH SPACES
, 2008
"... ABSTRACT. In this paper, we show the triangle inequality and its reverse inequality in quasiBanach spaces. ..."
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ABSTRACT. In this paper, we show the triangle inequality and its reverse inequality in quasiBanach spaces.
ON SOME GENERALIZED NORM TRIANGLE INEQUALITIES
"... Abstract. In this paper we characterize equality attainedness in some recently obtained generalized norm triangle inequalities. 1. ..."
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Abstract. In this paper we characterize equality attainedness in some recently obtained generalized norm triangle inequalities. 1.
SOME REMARKS ON THE TRIANGLE INEQUALITY FOR NORMS
"... Abstract. Remarks about strengthening of the triangle inequality and its reverse inequality in normed spaces for two and more elements are collected. There is also a discussion on Fischer–Muszély equality for nelements in a normed space. Some other estimates which follow from the triangle inequali ..."
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Cited by 5 (0 self)
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Abstract. Remarks about strengthening of the triangle inequality and its reverse inequality in normed spaces for two and more elements are collected. There is also a discussion on Fischer–Muszély equality for nelements in a normed space. Some other estimates which follow from the triangle
Relaxing the Triangle Inequality in Pattern Matching
 International Journal of Computer Vision
, 1996
"... . Any notion of "closeness" in pattern matching should have the property that if A is close to B, and B is close to C, then A is close to C. Traditionally, this property is attained because of the triangle inequality (d(A; C) d(A; B) + d(B; C), where d represents a notion of distance). Ho ..."
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Cited by 22 (0 self)
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. Any notion of "closeness" in pattern matching should have the property that if A is close to B, and B is close to C, then A is close to C. Traditionally, this property is attained because of the triangle inequality (d(A; C) d(A; B) + d(B; C), where d represents a notion of distance
Results 1  10
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100,721