The extreme points of a class of analytic functions with positive real part and a prescribed set of values

Let ζ = (0, z1, z2, …, zn) with |zj| < 1 for 1 ≤ j ≤ n, ω = (1,w1, w2, …,wn), and (ζ, ω) denote the set of functions p(z) that are analytic in D = {z : |z| < 1} and satisfy Rep(z) > 0 (|z| < 1), p(0) = 1, p(zj) = wj, j = 1, 2, …, n. In this article we investigate the extreme points of (ζ, ω).