### Derangements and Euler's difference table for ${C}_{l}\wr {S}_{n}$.

Faliharimalala, Hilarion L.M., Zeng, Jiang (2008)

The Electronic Journal of Combinatorics [electronic only]

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Faliharimalala, Hilarion L.M., Zeng, Jiang (2008)

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A class of non-linear singular integral equations with Hilbert kernel and a related class of quasi-linear singular integro-differential equations are investigated by applying Schauder's fixed point theorem in Banach spaces.

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Recently, A. W. Goodman introduced the class UCV of normalized uniformly convex functions. We present some sharp coefficient bounds for functions f(z) = z + a₂z² + a₃z³ + ... ∈ UCV and their inverses ${f}^{-1}\left(w\right)=w+d\u2082w\xb2+d\u2083w\xb3+...$. The series expansion for ${f}^{-1}\left(w\right)$ converges when $\left|w\right|<{\varrho}_{f}$, where $0<{\varrho}_{f}$ depends on f. The sharp bounds on $|{a}_{n}|$ and all extremal functions were known for n = 2 and 3; the extremal functions consist of a certain function k ∈ UCV and its rotations. We obtain the sharp bounds on $|{a}_{n}|$ and all extremal functions for...