Let $P\left(z\right)={\sum }_{\nu =0}^n{a}_{\nu }{z}^{\nu }$ be a polynomial of degree at most $n$ which does not vanish in the disk $\left|z\right|<1$, then for $1\le p<\infty$ and $R>1$, Boas and Rahman proved $${∥P\left(Rz\right)∥}_p\le ({∥R^n+z∥}_p/{∥1+z∥}_p){∥P∥}_p.$$ In this paper, we improve the above inequality for $0\le p<\infty$ by involving some of the coefficients of the polynomial $P\left(z\right)$. Analogous result for the class of polynomials $P\left(z\right)$ having no zero in $\left|z\right|>1$ is also given.

Kronecker sums and matricial norms are used in order to give a method for determining upper bounds for $\left|A\right|$ where $A$ is a latent root of a lambda-matrix. In particular, upper bounds for $\left|z\right|$ are obtained where $z$ is a zero of a polynomial with complex coefficients. The result is compared with other known bounds for $\left|z\right|$.

MSC 2010: 30A10, 30C10, 30C80, 30D15, 41A17.In the present article, I point out serious errors in a paper published in Mathematica Balkanica three years ago. These errors seem to go unnoticed because some mathematicians are applying the results stated in this paper to prove other results, which should not continue.

Mathematics Subject Classification: 26A33, 47A60, 30C15.In this paper we treat the question of existence and uniqueness of solutions of linear fractional partial differential equations. Along examples we show that, due to the global definition of fractional derivatives, uniqueness is only sure in case of global initial conditions.

Let D¯ denote the unit disk {z : |z| < 1} in the complex plane C. In this paper, we study a family of polynomials P with only one zero lying outside D¯. We establish criteria for P to satisfy implying that each of P and P' has exactly one critical point outside D¯.