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Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, vol.22, no.1, pp.27-31, 2006 (Scopus)
Let Ω be the class of functions w(z), |w(0) = 0, w(z)| < 1 regular in the unit disc D = {z : |z| < 1}. For arbitrarily fixed numbers A ∈ (-1, 1], B ∈ [-1, A), 0 ≤ α < 1 let P(,4, B, α) be the class of regular functions p(z) in D such that p(0) = 1, and which is p(z) ∈ P(A, B, α) if and only if p(z) = 1+[(1 - α) A+αB]w(z)/1+Bw(z) for some function w(z) ∈ Ω and every 5 ∈ D. In the present paper we apply the principle of subordination ([1], [3], [4], [5]) to give new proofs for some classical results concerning the class S*(A, B, α) of functions f(z) with f(0) = 0, f′(0) = 1, which are regular in D satisfying the condition: f(z) ∈ S*(A, B, α) if and only if z f′/f(z) = p(z) for some p(z) ∈ P(A, S, α) and for all z in D.