The Zalcman Conjecture for Close-to-Convex Functions
The Zalcman Conjecture for Close-to-Convex Functions
Let $S$ be the class of functions $f(z) = z + \cdots$ analytic and univalent in the unit disk $D$. For $f(z) = z + {a_2}{z^2} + \cdots \in S$, Zalcman conjectured that $|a_n^2 - {a_{2n - 1}}|\; \leq \;{(n - 1)^2}(n = 2,3, \ldots )$. This conjecture is verified …