The Hausdorff dimension of Julia sets of meromorphic functions II

A family of transcendental meromorphic functions, f(p)(z), p is an element of N is considered. It is shown that, if p greater than or equal to 6, then the Hausdorff dimension of the Julia set of lambda f(p) satisfies dim J(lambda f(p)) less than or equal to 1/p, for 0 < lambda < 1/6(p), and dim J(lambda f(p)) greater than or equal to 1 - (30 In In p/ln p), for p(4p-1)/10(5) ln p < lambda < p(4p-1)/10(4) ln p. These results are used elsewhere to show that, for each d is an element of(0, 1), there exists a transcendental meromorphic function for which dim J(f) = d.