Periodic Functions
In discrete time, a function is period if there exists an integer N such that x[n+N] = x[n]
An example of a discrete period function would be $ e^j*w*n) $
In continuous time, a function x(t) is periodic if there exists a T>0 such that x(t+T) = x(t)
Non Periodic Functions
All functions that are not periodic I suppose would then be Non-periodic.