Star Coloring of Subcubic Graphs

T. Karthick; C.R. Subramanian

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Uniformly convex functions II

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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 $f^{- 1} (w) = w + d ₂ w ² + d ₃ w ³ + . . .$ . The series expansion for $f^{- 1} (w)$ converges when $| w | < ϱ_{f}$ , where $0 < ϱ_{f}$ 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...

Existence results for non-linear singular integral equations with Hilbert kernel in Banach spaces

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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.

On potentially $H$ -graphic sequences

Meng Xiao Yin, Jian Hua Yin (2007)

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For given a graph $H$ , a graphic sequence $π = (d_{1}, d_{2}, ..., d_{n})$ is said to be potentially $H$ -graphic if there is a realization of $π$ containing $H$ as a subgraph. In this paper, we characterize the potentially $(K_{5} - e)$ -positive graphic sequences and give two simple necessary and sufficient conditions for a positive graphic sequence $π$ to be potentially $K_{5}$ -graphic, where $K_{r}$ is a complete graph on $r$ vertices and $K_{r} - e$ is a graph obtained from $K_{r}$ by deleting one edge. Moreover, we also give a simple necessary and sufficient condition...