2017/08/16 by Mehrez, Khaled, Sitnik, Sergei M.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.1708.06611
In this paper, our aim is to show 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 monotonicity of ratios for sections of series of Fox-Wright functions, the results is also closely connected with Turán--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.