Let P denote the well-known class of Carathéodory functions of the form p(z) = 1 + c1z + . . ., z ∈ ∆ = {z ∈ : |z| < 1}, with positive real part in the unit disc and let H(M) stand for the class of holomorphic functions commonly bounded by M in ∆. In 1992, J. Fuka and Z. J. Jakubowski began an investigation of families of mappings p ∈ P fulfilling certain… (More)