The author [J. Math. Anal. Appl. 319, No. 2, 450--459 (2006; Zbl 1091.33002)] has shown for the ratio \(m(s) = F(a,b,a+b,1-r^2)/F(a,b,a+b,r^2)\) of hypergeometric functions, \[ \sqrt{(m(r)m(s))} \leq m(\sqrt{(rs))}, \quad a, b > 0,\quad r, s\in (0,1). \] In this paper, the author has shown an analogous result and other such inequalities hold for hypergeometric functions also (not only for their ratios). The author also determines some conditions for the parameters of generalized and normalized Bessel functions, Kummer functions and for some power series to have inequalities.