Inspect your roof carefully especially around the suspected leak areas. If the leaks have caused damage you will feel rotted wood beneath the roofing material. It will be really soft.
If you have rotted wood, the cheap way to go would be number 2 & 3 below. This will seal the leaks and provide protection for a few years. It will not help the value of your RV when it comes time to sell it.
The best fix would be to remove the roofing material to determine the extent of the damage. Repair the damage and then have the bedliner sprayed on the entire roof (number 1 below). Expensive solution. I would only do this if I planned to keep the RV for 10 years.
If little or no rotten wood- You have several options:
1- Recover the entire roof with a new membrane or spray on material like the bedliner for pick up trucks. Many RV'ers are going this route. Both are expensive
2- After washing the roof and letting it dry- Re-seal all seams with EternaBond tape and sealant. This is the least expensive option and may take care of all current and future leaks.
3- To further protect your roof after number 2 you can use a two step roof sealant. This provides basically a new roof membrane for many years of protection. Cheaper than number 1