  In this paper some Tur\'an type inequalities for classical and generalized
Mittag-Leffler functions are considered. The method is based on proving
monotonicity for special ratio of sections for series of Mittag-Leffler
functions. Some applications are considered to Lazarevi\'c and Wilker-type
inequalities for classical and generalized Mittag-Leffler functions. At the end
some open problems are formulated.
