Conditions for Carathéodory Functions
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چکیده
then we say that p is the Catathéodory function. LetA denote the class of all functions f analytic in the open unit disk U {z : |z| < 1} with the usual normalization f 0 f ′ 0 − 1 0. If f and g are analytic in U, we say that f is subordinate to g, written f ≺ g or f z ≺ g z , if g is univalent, f 0 g 0 and f U ⊂ g U . For 0 < α ≤ 1, let STC α and STS α denote the classes of functions f ∈ A which are strongly convex and starlike of order α; that is, which satisfy
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