6 problems

Monotonic-components conjecture. If ${\bf X}\circ{\bf T}$ is not itself a Lévy process, then it can be mimicked by a Lévy process if and only if ${\bf T}$ has monotonic components.

Ruscheweyh–Salinas conjecture. The function $v_{\lambda}(1,-1,z)$ is stable with respect to itself for $0<\lambda<1/2$. This extends their proved case $\lambda=1/2$, which is conne…

Koumandos–Ruscheweyh conjecture. For $0<\mu\leq\mu^{\ast}(\rho)$ and every $n\in\mathbb{N}$,

Campbell's conjecture. The conclusion of Theorem 3, namely $|f'(z)|\leq|F'(z)|$ for $|z|\leq n(\alpha)$, with $\alpha=\alpha(\mathcal{U}_\alpha)$, holds for

Largest-parameter positivity conjecture. The inequality

Let ${\mathcal K}(\alpha)$ denote the class of normalized analytic functions that are convex of order $\alpha$, and let $k_\alpha$ be characterized by … with $k_\alpha(0)=0$ and…