I am hoping that this question (if in acceptable form) be community wiki.
Are there any open conjectures in real analysis primarily targeting real valued functions of a single real variable ? (it may involve other concepts but primarily targeting these type of functions and no involvement of number theory). Its not that i am going to attack them right away ( not due to lack of interest but time) but am just curious to know them. Also how difficult it is get a new result in this area ?