August 10, 2010
August 1, 2010
Problem 045 (Van Khea)
Let be positive real numbers and satisfying . Prove that if and then we have
Proof
We have
Let
Let
From the inequality by Van Khea for and we have
Example1: Let then we have
Example2: Let then we have
See also the inequality by Van Khea
Problem 044
Let be positive real numbers and satisfying . Prove that:
-
If then we have
-
If then we have
Proof
We have
Let
-
If then So from the inequality by VanKhea for
and we get
-
If then we have So from the inequality by Van Khea for and we get:
Van Khea
See also the inequality by van khea
Problem 041
Let and . For be positive real numbers and satisfying . Prove that:
Van Khea
Problem 040
Let and . For be positive real numbers and satisfying . Prove that:
Van Khea
Problem 039
Let and . For be positive real numbers and satisfying ; Prove that:
Proof
From the problem 038 we have
From Jensen’s inequality for we have
Therefore the proof is completed.
Van Khea
Problem 038
Let and . For all ; Prove that:
Proof
Let but we have
From the inequality by van khea for and we have
Therefor the proof is completed.
Van Khea