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