Functional inequalities for the Fox–Wright functions

In this paper, our aim is to establish some mean value inequalities for the Fox–Wright functions, such as Turán-type inequalities, Lazarević 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 the monotonicity of ratios for sections of series of Fox–Wright functions. The results are also closely connected with Turán-type inequalities. Moreover, some other type inequalities are also presented. At the end of the paper, some problems are stated which may be of interest for further research.