Can you equip UPS orInverter for Mail server to have 24 hr Backup?

Yes you can use a UPS provided it can supply enough power for the server and you have good battery backup.

A inverter is an option but a little bit more complicated, you will need a good battery charger and you have to run the server on the inverter alone, so the inverter will work 24/24 because you can not use mains supply to the server, so it have to be a good quality inverter, preferably a sine wave inverter with a 100% duty cycle, good batteries and a good charger that will supply enough charge to maintain the current draw of the inverter and have reserve to store energy in the batteries for times when the mains is out and the charger can not supply the energy demand.