Let (Ω,,P) be a probability space and let τ: ℝ × Ω → ℝ be strictly increasing and continuous with respect to the first variable, and -measurable with respect to the second variable. We obtain a partial characterization and a uniqueness-type result for solutions of the general linear equation $F\left(x\right)={\int }_{\Omega }F\left(\tau (x,\omega )\right)P\left(d\omega \right)$ in the class of probability distribution functions.

Let (Ω,,P) be a probability space and let τ: ℝ × Ω → ℝ be a mapping strictly increasing and continuous with respect to the first variable, and -measurable with respect to the second variable. We discuss the problem of existence of probability distribution solutions of the general linear equation $F\left(x\right)={\int }_{\Omega }F\left(\tau (x,\omega )\right)P\left(d\omega \right)$. We extend our uniqueness-type theorems obtained in Ann. Polon. Math. 95 (2009), 103-114.

We present a new method of analytic continuation of series out of their disk of convergence. We then exhibit a connection with the phenomenon of bifurcation delay in a planar discrete dynamical system; the limit of the method is then related to a stop phenomenon.

Let $f$ be a transcendental meromorphic function. We propose a number of results concerning zeros and fixed points of the difference $g\left(z\right)=f(z+c)-f\left(z\right)$ and the divided difference $g\left(z\right)/f\left(z\right)$.