The fatigue stress is described by the stress range. That is the difference between the maximum and the minimum stress under one load cycle. Note also that the amplitude is half the stress range.
The mean stress and the maximum stress are of secondary interest. Of course you also need to check the static load, then the materials yield strength is compared to the static maximum stress from the load of the structure.
Remember that it is the stress range that describes fatigue stress.
Picture 1: The stress range definition