ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS { N. 41{2019 (284-289) 

A CONCISE PROOF OF A DOUBLE INEQUALITY INVOLVING

 THE EXPONENTIAL AND LOGARITHMIC FUNCTIONS

Huan-Nan Shi，Shan-He Wu

Abstract. In this note we provide a concise proof for a double inequality involving
the exponential and logarithmic functions, our method is based on the usage of the
majorization inequalities and the Schur-convexity of a function.

Keywords: inequality, exponential function, logarithmic function, Schur-convexity,
majorization inequality, Stolarsky mean.

A concise proof of a double inequality involving the exponential and logarithmic.pdf