Lyn, yours are beardless iris. Were they planted as bulbs? If so they are probably iris hollandica (Dutch iris), and have different growing needs than the bearded iris that grow from rhizomes at the top of the soil.
For the Dutch iris: Fertilize them as you would other bulbs (tulips/daffodils, etc.) and they should do well. The foliage from my Dutch iris dies back in the summer. It is okay to cut it off/mow over it at this stage because new growth will pop back up in the spring (just like daffodils). Some people have said that the Dutch iris will dwindle over time, but if you feed them a couple times of year they should keep coming back year after year. Mine have survived gobs of neglect but never quit coming back.
