Value distribution of meromorphic solutions of certain difference Painleve III equations

In this paper, we investigate the difference Painleve III equations w(z + 1)w(z - 1)(w(z) - 1)(2) = w(2) (z) - lambda w(z) + mu(lambda mu not equal 0) and w(z + 1)w(z - 1)(w(z) - 1)(2) = w(2)(z), and obtain some results about the properties of the finite order transcendental meromorphic solutions. In particular, we get the precise estimations of exponents of convergence of poles of difference Delta w(z) = w(z + 1) - w(z) and divided difference Delta w(z)/w(z), and of fixed points of w(z + eta) (eta is an element of C \ {0}).