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Let ζ = (0, z 1 , z 2 , …, z n ) with | z j | j ≤ n , ω = (1, w 1 , w 2 , …, w n ), and (ζ, ω) denote the set of functions p ( z ) that are analytic in D = { z : | z | z ) > 0 (| z | p (0) = 1, p ( z j ) = w j , j = 1, 2, …, n . In this article we investigate the extreme points of (ζ, ω).

Let C′(α,β) be the class of functions f ( z ) = z + ∑ n = 2 ∞ a n z n analytic in D = { z : | z | 1 } , satisfying for some convex function g(z) with g(0)=g′(0) − 1 = 0 and for all z in D the condition | z f ' ( z ) g ( z ) - 1 z f ' ( z ) g ( z ) + ( 1 - 2 α ) | β for some α, β (0≤α