An Klamkin Type Inequality on the Triangle

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Chu, Xiao-Guang and Zhang, Zhi-Hua (2005) An Klamkin Type Inequality on the Triangle. Research report collection, 8 (1).


In this short note, we give a new Klamkin type inequality on the triangle: for any point P inside the triangle ABC, then (x + y + z)(xK₁² + yK₂² + zK₃²) ≥ a²yz + b²zx + c²xy where x, y, z are three real numbers, a, b, c the sides of triangle ABC and K₁ = XD,K₂ = Y E,K₃ = ZF if X, Y,Z and D,E, F are the midpoints of PA, PB, PC and BC,CA,AB respectively.

Item type Article
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords Klamkin type inequality, triangle
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