We consider the family P(1, b), b > 0, consisting of functions p analytic in the open unit disc U with the normalization p(0) = 1 which have the disc formulation |p − 1| < b in U. Applying the subordination properties to certain choices of p using the functions fn(z) = z + ∑∞ k=1+n akz , n = 1, 2, ..., we obtain inclusion relations, sufficient starlikeness and convexity conditions, and coeffici...
