منابع مشابه
Reverse Inequalities of Erdös–mordell Type
This paper deals with the reverse inequalities of Erdös-Mordell type. Our result contains as special case the following reverse Erdös-Mordell inequality: R1 +R2 +R3 < √ 2 (ρ1 +ρ2 +ρ3) , where Ri and ρi (i=1, 2, 3) denote respectively the distances from an interior point Q of A1A2A3 to the vertexes A1, A2, A3 and to the circumcenters of A2QA3 , A3QA1 , A1QA2 . Some other closely related inequali...
متن کاملErdős-Mordell-Type Inequalities in a Triangle
with equality if and only if the triangle is equilateral and P is its center. This inequality was conjectured by Erdős [1] and proved by Mordell and Barrow [2]. Oppenheim [3] established a number of additional inequalities relating the six distances p, q, r , x , y, and z. Such an inequality will be referred to as an Erdős-Mordell-type inequality. A survey of some of these inequalities can be f...
متن کاملOn the Extension of the Erdös–mordell Type Inequalities
We discuss the extension of inequality RA c a rb + b a rc to the plane of triangle ABC . Based on the obtained extension, in regard to all three vertices of the triangle, we get the extension of Erdös-Mordell inequality, and some inequalities of Erdös-Mordell type. Mathematics subject classification (2010): 51M16, 51M04, 14H50.
متن کاملOn reverse Hilbert-type inequalities
*Correspondence: [email protected] 1School of Mathematical Science, Huaibei Normal University, Huaibei, 235000, P.R. China Full list of author information is available at the end of the article Abstract By introducing two pairs of conjugate exponents and estimating the weight coefficients, we establish reverse versions of Hilbert-type inequalities, as described by Jin (J. Math. Anal. Appl. 340:...
متن کاملChvátal-Erdös type theorems
The Chvátal-Erdös theorems imply that if G is a graph of order n ≥ 3 with κ(G) ≥ α(G), then G is hamiltonian, and if κ(G) > α(G), then G is hamiltonian-connected. We generalize these results by replacing the connectivity and independence number conditions with a weaker minimum degree and independence number condition in the presence of sufficient connectivity. More specifically, it is noted tha...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2009
ISSN: 1331-4343
DOI: 10.7153/mia-12-31