ABOUT SOME POWER SERIES INEQUALITIES AND TRACE INEQUALITIES

The aim of this paper is to present: several new inequalities for power series with real coefficients by using a Young-type inequality for sequences of complex numbers, a matrix analogue for the Hilbert-Schmidt norm and a trace inequality for positive operators in Hilbert spaces, starting from a refinement of the classical Kittaneh-Manasrah inequality. Then several consequences as applications will be presented for special functions such as polylogarithm and for elementary functions.