Answering my own new and more detailed question rather than an existing one

Question

Recently I have posted this question:

Functions that preserve asymptotic equivalence.

I searched MSE and MO sites for related questions before asking, but didn't succeed, my bad. After few days, I encountered this old question, a little less specific than mine, but asking about same things:

What operations is this asymptotic relation closed under?

The OP has been inactive for 4 years and hasn't accepted any answer. He's probably left the site forever.

Answers the question already had seemed somehow incomplete to me. But them helped me develop my own solution which, in my opinion, completely does for my question.

What should I do: answer my own question and mark the old one as duplicate or, conversely, answer (and edit) the old question and close the new?

UPDATE. I've posted answer to the new question and a comment to the old, as was suggested here. Other opinions and comments on subject are still welcome.

Answer 1

Answer your own question but don't mark the old one as duplicate,because it is not. Instead you can add a comment to the old question which says there is an answer to the question here.