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Question: How to determine convexity of this function?

Question:How to determine convexity of this function?

Markiyan Hirnyk 7759 Maple
convex
June 14 2014
0
This question is related to the Post convexity

Let us consider the expression

restart;
f := log[x](1+(x^a-1)*(x^b-1)/(x-1));
Does it define a convex function on the interval 0..1 and on the interval 1..infinity if the parameters a>0, a< 1, b >0, b <1?

My try is

and

.

At the same time I have got problems in the general case. For example,

Error, (in @) too many levels of recursion

and

That's all right if

convex.mw

 

 
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