I recently read a paper, which posed some interesting questions in a section named further research.
They concluded the section by writing, "we leave all these questions for our future research".
I am really interested in one of the questions, is it considered inappropriate to write a paper handling one of those questions? The pronoun "our" indicates that the author wish to dig in to this question himself. However the paper was published in 2012, and by browsing the authors personal webpage I get no sign of a paper like that in progress.
In case I wish to write a paper on that particular topic, should I notify the author who posed the question? (Say, by asking, is question X still open?)