Inequalities arising out of the value distribution of a differential monomial.
In this paper we obtain certain results for the polar derivative of a polynomial [...] , having all its zeros on [...] which generalizes the results due to Dewan and Mir, Dewan and Hans. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros.
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.
By combining Turán’s proof of Fabry’s gap theorem with a gap theorem of P. Szüsz we obtain a gap theorem which is more general then both these theorems.