Decking joist size - is 3x2 enough?

I’m looking at fitting decking over an existing brick path/patio.

Out of the back door there is a concrete step which drops down 100mm, ideally I want the deck to be at the same height (as close as possible give or take a few mm) as the step so the only way to do this would be with 3x2 joists with the decking over the top but I’m not sure if there will be too much flex in the deck with this size timber?

The path by the back door is 1m wide by just over 3m long, then this joins onto the larger section of patio which is 3.5m wide by 5m long and I’d prefer to have this all at the same height rather than stepping it.

Any advice would be much appreciated.

 

Rough sketch of the area/shape, more frequent supports isn’t too much of an issue if it works