Li, Da-Mao; Shi, Huan-Nan Schur convexity and Schur-geometrically concavity of generalized exponent mean. (English) Zbl 1177.26040 J. Math. Inequal. 3, No. 2, Article ID 22, 217-225 (2009). Summary: The monotonicity, the Schur-convexity and the Schur-geometrically convexity with variables \((x,y)\) in \(\mathbb R_{++}^2\) for fixed a of the generalized exponent mean \(I_a(x,y)\) is proved. Besides, the monotonicity with parameters \(a\) in \(\mathbb R\) for fixed \((x,y)\) of \(I_a(x,y)\) is discussed by using the hyperbolic composite function. Furthermore, some new inequalities are obtained. Cited in 4 Documents MSC: 26D15 Inequalities for sums, series and integrals 26A51 Convexity of real functions in one variable, generalizations Keywords:monotonicity; hyperbolic function PDFBibTeX XMLCite \textit{D.-M. Li} and \textit{H.-N. Shi}, J. Math. Inequal. 3, No. 2, Article ID 22, 217--225 (2009; Zbl 1177.26040) Full Text: Link