A note on Turلn type and mean inequalities for the Kummer function

Turán-type inequalities for combinations of Kummer functions involving Φ ( a ± ν , c ± ν , x ) and Φ ( a , c ± ν , x ) have been recently investigated in [Á. Baricz, Functional inequalities involving Bessel and modified Bessel functions of the first kind, Expo. Math. 26 (3) (2008) 279–293; M.E.H. Ismail, A. Laforgia, Monotonicity properties of determinants of special functions, Constr. Approx. 26 (2007) 1–9]. In the current paper, we resolve the corresponding Turán-type and closely related mean inequalities for the additional case involving Φ ( a ± ν , c , x ) . The application to modeling credit risk is also summarized.