The Fake Frying Pan is a weapon in Mother 3 that is equippable by Kumatora. It can be purchased for 18000 DP in New Pork City. It only increases her offense stat by 26.
It is intended as a reference to the weapon of choice for female characters in previous games (Ana in EarthBound Beginnings and Paula in EarthBound), which was the frying pan.
You can buy this item in the New Pork Theatre in New Pork City.