Exponential Inequalities in Calibration Problems with Gaussians Errors

The proof of three power-exponential inequalities

“…The power-exponential functions have useful applications in mathematical analysis and in other theories like Statistics [1], Biology [2,3], Optimization [4], Ordinary Differential equations [5] and Probability [6]. In the recent years there is a intensive research in this area, see for instance [7,8,9,10,11,12,13,14,15,16,17] and the recent overview on general mathematical inequalities done by Cerone and Dragomir [18].…”