PROOFS OF THREE OPEN INEQUALITIES WITH POWER-EXPONENTIAL FUNCTIONS


Authors

VASILE CIRTOAJE - Department of Automatic Control and Computers, University of Ploiesti, Romania.


Abstract

The main aim of this paper is to give a complete proof to the open inequality with power-exponential functions \[a^{ea} + b^{eb} \geq a^{eb} + b^{ea},\] which holds for all positive real numbers a and b. Notice that this inequality was proved in [1] for only \(a \geq b \geq \frac{1}{ e}\) and \(\frac{1}{ e} \geq a \geq b\).In addition, other two open inequalities with power-exponential functions are proved, and three new conjectures are presented.


Keywords


MSC


References