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Titlebook: Recent Advances in Geometric Inequalities; D. S. Mitrinovi?,J. E. Pe?ari?,V. Volenec Book 1989 Springer Science+Business Media Dordrecht 1

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21#
發(fā)表于 2025-3-25 07:11:31 | 只看該作者
22#
發(fā)表于 2025-3-25 09:55:04 | 只看該作者
Homogeneous Symmetric Polynomial Geometric Inequalities, the form p(a, b, c) 0 or p(a, b, c) 0 where p(a, b, c) is a symmetric and homogeneous polynomial of degree n in the real variables a, b, c representing the sides of a triangle. They gave the general solution for such inequalities if n ≤ 3.
23#
發(fā)表于 2025-3-25 13:54:14 | 只看該作者
Some Other Transformations,n use these results for generating many other inequalities, i.e. using any known inequality for the sides of a triangle ., and any result from I.3, we get the inequality ., where a., b., c. are the sides of a new triangle given as in I.3.
24#
發(fā)表于 2025-3-25 18:33:14 | 只看該作者
25#
發(fā)表于 2025-3-25 22:57:07 | 只看該作者
Homogeneous Symmetric Polynomial Geometric Inequalities, the form p(a, b, c) 0 or p(a, b, c) 0 where p(a, b, c) is a symmetric and homogeneous polynomial of degree n in the real variables a, b, c representing the sides of a triangle. They gave the general solution for such inequalities if n ≤ 3.
26#
發(fā)表于 2025-3-26 00:43:15 | 只看該作者
27#
發(fā)表于 2025-3-26 07:16:07 | 只看該作者
28#
發(fā)表于 2025-3-26 10:51:23 | 只看該作者
Special Triangles,ng a. + b. + c. = 8R. is a right triangle. Starting from these well-known properties V. Devidé [1] has investigated at length the special class of triangles defined by a. + b. + c. = 6R.. O. Bottema [2] considered the general class of triangles (k-triangles) defined by a. + b. + c. = kR.. In [12] it
29#
發(fā)表于 2025-3-26 12:37:22 | 只看該作者
30#
發(fā)表于 2025-3-26 20:35:20 | 只看該作者
Some Trigonometric Inequalities, that many of these inequalities are still valid for real numbers A, B, C which satisfy the condition . where p is a natural number (which has to be odd in some cases). This also applies to the inequality of M. S. Klamkin [2] which can be specialized in many ways to obtain numerous well known inequalities.
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