An Upper Bound Estimate for H. Alzer’s Integral Inequality

Authors

Chu Yuming Department of Mathematics, Huzhou Teachers College, Huzhou, P. R. China
Zhang Xiaoming Haining Radio and TV University, Haining, P. R. China
Tang Xiaomin Department of Mathematics, Huzhou Teachers College, Huzhou, P. R. China

Convex function, integral inequality, logarithmic mean

We get an upper bound estimate for H. Alzer's integral inequality. As applications, we obtain some inequalities for the logarithmic mean.

2000 Mathematics Subject Classification. 26D07

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T. Zgraja, On continuous convex or concave functions with respect to the logarithmic mean, Acta Univ. Carolin. Math. Phys., 46 (2005), 3–10.

J. Matkowski, Affine and convex functions with respect to the logarithmic mean, Colloq. Math., 95 (2003), 217–230.

C. E. M. Pearce, J. Peˇcari´c, Some theorems of Jensen type for generalized logarithmic means, Rev. Roumaine Math. Pures Appl., 40 (1995), 789–795.

J. S´andor, On the identric and logarithmic means, Aequationes Math., 40 (1990), 261–270.

C. O. Imoru, The power mean and the logarithmic mean, Internat. J. Math. Math. Soc., 5 (1982), 337–343.

K. B. Stolarsky, The power and logarithmic means, Amer. Math. Monthly, 87 (1980), 545–548.

T. P. Lin, The power mean and the logarithmic mean, Amer. Math. Monthly, 81 (1974), 879–883.

B. C. Carlson, The logarithmic mean, Amer. Math. Monthly, 79 (1972), 615–618.

H. Alzer, On an integral inequality, Anal. Num´er. Th´eor. Approx., 18 (1989), 101–103.