How to expression the function

Variable is x and y,both of them are scalar.How do I express the multiplication of two convex functions

Please provide how it appears in your model. In the objective or in a constraint?

Also how did you conclude the resulting optimization model is convex? What is your proof of that?

Sorry, I found that I made a mistake. My new function is this. It has been proved in other literatures that it is strictly convex in (0, x0). Can this be represented by CVX?

Assuming a,b,c>0 then it looks convex for all B>=0 e.g.

Thank you very much!

But I should how to expression it?It always shows real*log (convex).

You or someone has to figure out a formulation that is CVX i.e. DCP compliant.

Given the function is convex then it might be possible that such a reformulation exist.
I do not know what it is as I write this.