OP, honestly, I don't think there is any definitive answer to your question. TSA doesn't explicitly list "frying pan" as either allowed or disallowed because it's something not commonly found in carryons, and they can't possibly list thousands of items. Without it explicitly on any list, it will be up to the discretion (or whim, if you prefer) of the individual TSA agent who screens your carryon. If the TSA agent chooses to view it as a harmless cooking item, then it will be allowed. It the TSA agent chooses to view it as a "weapon" (analogous to a club), then it will be forbidden. Realistically, nobody can give the quantitative probabilities of these two outcomes with high confidence.

If you're talking about a rather large and heavy (such as cast iron) frying pan, I could definitely see a TSA agent forbidding it to pass screening.