arXiv subjects
Publications and source records attributed to Derek K. Thomas.
For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also suggest some significant open problems.
For $f\in \mathcal{S}$, the class of normalized functions, analytic and univalent in the unit disk $\mathbb{D}$ and given by $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$ for $z\in \mathbb{D}$, we give an upper bound for the coefficient difference $|a_4|-|a_3|$ when $f\in \mathcal{S}$. This provides an improved bound in the case $n=3$ of Grispan's 1976 general bound $||a_{n+1}|-|a_n||\le 3.61\dots .$ Other coefficients bounds, and bounds for the second and third Hankel determinants when $f\in \mathcal{S}$ are found when either $a_2=0,$ or $a_3=0$.