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.


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ISRP Style

VASILE CIRTOAJE, PROOFS OF THREE OPEN INEQUALITIES WITH POWER-EXPONENTIAL FUNCTIONS, Journal of Nonlinear Sciences and Applications, 4 (2011), no. 2, 130-137

AMA Style

CIRTOAJE VASILE, PROOFS OF THREE OPEN INEQUALITIES WITH POWER-EXPONENTIAL FUNCTIONS. J. Nonlinear Sci. Appl. (2011); 4(2):130-137

Chicago/Turabian Style

CIRTOAJE, VASILE. "PROOFS OF THREE OPEN INEQUALITIES WITH POWER-EXPONENTIAL FUNCTIONS." Journal of Nonlinear Sciences and Applications, 4, no. 2 (2011): 130-137


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