On Shafer and Carlson inequalities.
On Shafer-Fink-type inequality.
On some polynomial-like inequalities of Brenner and Alzer.
On the cyclic homogeneous polynomial inequalities of degree four.
On the Erdös-Debrunner inequality.
On the inequality of P. Turán for Legendre polynomials.
On the maximum modulus of a polynomial and its derivatives.
On the proof of Erdős' inequality
Using undergraduate calculus, we give a direct elementary proof of a sharp Markov-type inequality for a constrained polynomial of degree at most , initially claimed by P. Erdős, which is different from the one in the paper of T. Erdélyi (2015). Whereafter, we give the situations on which the equality holds. On the basis of this inequality, we study the monotone polynomial which has only real zeros all but one outside of the interval and establish a new asymptotically sharp inequality.
On the strengthened Jordan's inequality.