This paper studies the convergence of periodic mapping and periodic probability mapping using periodic iterative g-contraction mapping theorem. The main results are: 1, one fixed point  of exponential function type is found; 2, as a new member of family of density functions, two related fixed points  with sine, cosine types are constructed. Application of periodic mapping with two fixed points of sine, cosine types to the analysis of share’s price is given.

periodic mapping, probability Banach space,probability of probability, periodic probability mapping, periodic iterative g-contractive mapping theorem.