# open conjectures in real analysis targeting real valued functions of a single real variable

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 ?

• I hope this gets some interesting answers! Aug 20, 2011 at 13:07
• Why did you accept an answer already? There probably are many more open problems. Aug 21, 2011 at 16:25
• @Jonas Teuwen : The current answer by Gerry Myerson gives some pertinent examples. I have just accepted, but if by doing so it prevents others from giving more answers ( may be by not appearing on the main page or some such thing), I'd rather wait. But i really do not understand how to select answer in case of mutiple answers giving suitable examples as this question itself is not very specific. More over if you say that it should be done based on the importance of the examples then probably i am not qualified to do such a thing. I hope there would be a discussion which takes care of it. Aug 21, 2011 at 16:42
• I agree with Jonas that you shouldn't be so quick to accept an answer. Wait until things settle down. As to which answer to accept if/when there are many answers given, just accept the one that you personally find most useful. Your vote will be read that way, and not as a judgement from on high as to which answer presents the most important examples. Aug 24, 2011 at 1:13
• It would appear that things have settled down. Maybe it's time to accept an answer. Oct 25, 2013 at 10:08

Khabibullin’s conjecture on integral inequalities. Also, according to this entry at the Open Problem Garden, the following question is open: Give a necessary and sufficient criterion for the sequence $a_n$ so that the power series $\sum a_nx^n$ is bounded for all $x$ in $\bf R$.