Functional inequalities for Fox-Wright functions

In this paper, our aim is to show some mean value inequalities for the Fox-Wright functions, such as Tur'an–type inequalities, Lazarevi'c and Wilker–type inequalities. As applications we derive some new type inequalities for hypergeometric functions and the four–parametric Mittag–Leffler functions. Furthermore, we prove monotonicity of ratios for sections of series of Fox-Wright functions, the results is also closely connected with Tur'an–type inequalities. Moreover, some other type inequalities are also presented. At the end of the paper, some problems stated, which may be of interest for further research.