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By using the basic logarithmic inequality ln x ≤ x − 1 we deduce integral inequalities, which particularly imply the inequalities G < L < A for the geometric, logarithmic, resp. arithmetic means.
- Logaritmic function
- Logarithmic mean
- Means and their inequalities
- Carlson, B. C. (1966) Some inequalities for hypergeometric functions, Proc. Amer. Math.Soc.,17, 32–39
- Carlson, B. C. (1972) The logarithmic mean, Amer. Math. Monthly, 79, 615–618.
- Ostle, B., & Terwilliger, H. L. (1957) A comparison of two means, Proc. Montana Acad.Sci., 17, 69–70.
- Sándor, J. (1990) On the identric and logarithmic means, Aeq. Math., 40, 261–270.
- Lorenzen, G. (1994) Why means in two arguments are special, Elem. Math., 49, 32–37.
Cite this paperAPA
Sándor, J. (2015). A basic logarithmic inequality, and the logarithmic mean. Notes on Number Theory and Discrete Mathematics, 21(1), 31-35.Chicago
Sándor, József. “A Basic Logarithmic Inequality, and the Logarithmic Mean.” Notes on Number Theory and Discrete Mathematics 21, no. 1 (2015): 31-35.MLA
Sándor, József. “A Basic Logarithmic Inequality, and the Logarithmic Mean.” Notes on Number Theory and Discrete Mathematics 21.1 (2015): 31-35. Print.