Preheat the oven to 190 degrees C. Grease a 12 cup muffin tin or line with paper muffin liners.
In a large bowl stir together the flour, sugar substitute, baking powder, bicarb soda and cinnamon. In a separate bowl mix together the egg whites, mashed banana and apple sauce. Add the wet ingredients to the dry and mix until just blended. Fill prepared muffin cups 3/4 full.
Bake for 15 to 18 minutes in the preheated oven, or until the top springs back when lightly touched. Allow muffins to cool in the pan over a wire rack for a little while before tapping them out of the pan.