Theoreom:
(Van Khea):Let . Prove that:
Let and such that . We get:
Let and for such that: . So we get:
Theoreom:
(Van Khea) :Let be positive real numbers and let
. For all be real numbers satisfying and . So we have:
Equality hold when:
Theoreom:
(Van Khea): For a real convex fruction numbers in its domain , and positive so we can write that:
For a real concave fruction numbers in its domain , and positive so we can write that:
Theoreom:
(Van Khea): Let be positive real numbers and satisfying . So we have:
Theoreom:
(Van Khea): Let . So we have
Theoreom:
(Van Khea): Let be positive real numbers and for all satisfy . So we have:
និង
Theorem:
(Van Khea) :1/ Let a real convex function for all in its domain. Suppose that for all positive real numbers satisfies in its domain and . Then we have:
.
2/ Let a real concave function for all in its domain. Suppose that for all positive real numbers satisfies in its domain and . Then we have:
.
Theorem:
(Van Khea): Let is a convex function. For any positive real numbers that and . So for we can stat as:
Special case:
- If
- If then
Theorem:
(van khea): 1/ Let be positive real numbers such that . So we have:
(van khea):2/ Let be positive real numbers such that . So we have:
Theoreom:
(van khea): Let be positive real numbers such that: or .Then
Theoreom:
(van khea): Let be positive real numbers such that: or .Then
Theoreom:
(van khea): Consider where and or . Let be convex function or momotonic and let where in the same neture. Then:
Theoreom:
(van khea): Consider where and or . Let be convex function or momotonic and let where in the same neture. Then:
Theorem:
(van khea): Let then we have:
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