The authors investigate the log convexity with respect to the parameter \(\gamma\), of the zeros of the generalized Airy functions, which are solutions of the differential equation \((1)\;y''+x^ \gamma y=0,\;x>0\). The results are established using several known facts about the zeros of the Bessel functions. This is possible because equation (1) is connected with the Bessel differential equation by means of a suitable transformation. As an application of the results the lower bound \[ j_{\nu_ 1}>2\nu\exp({\log\pi-0.18522({1\over\nu}-2) \over 2\nu}), 0<\nu <1/2 \] is obtained. Here \(j_{\nu_ 1}\) denotes the first positive zero of the Bessel function of the first kind.