Abstract
We consider the Fekete-Szegö problem with real parameter $λ$ for the class $Co(α)$ of concave univalent functions.
Coefficient bounds & claims (5)
Machine-extracted from the paper text - useful for cross-referencing, not a verified fact.
coefficient_bound
a3 - lambda*a2^2 ≤ 2*alpha**2/3 + 1/3 - lambda*alpha**2 for class Co(alpha) (sharp) [Theorem (Case 1 and Cases A-C)]
coefficient_bound
a3 - lambda*a2^2 ≤ (alpha*(10 - 9*lambda) - (3*lambda - 2)) / (9*(2 - lambda) + 3*alpha*(3*lambda - 2)) for class Co(alpha) (sharp) [Theorem (Cases D-E)]
coefficient_bound
a3 - lambda*a2^2 ≤ alpha*(1-lambda)*sqrt(12*(1-lambda)/((4-3*lambda)**2 - alpha**2*(3*lambda-2)**2)) for class Co(alpha) (sharp) [Theorem (Case F)]
coefficient_bound
a3 - lambda*a2^2 ≤ lambda*alpha**2 - 2*alpha**2/3 - 1/3 for class Co(alpha) (sharp) [Theorem (Case 2 and Case G)]
function_family
Class Co(alpha): f in A with f analytic in D, f(1)=infinity, f maps D onto a domain whose complement is convex, and the opening angle of f(D) at infinity is <= pi*alpha, alpha in (1,2]
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