Monotonicity of ratio between the generalized logarithmic means
نویسندگان
چکیده
منابع مشابه
Inequalities for Generalized Logarithmic Means
For p ∈ R, the generalized logarithmic mean Lp of two positive numbers a and b is defined as Lp a, b a, for a b, LP a, b b 1 − a 1 / p 1 b − a 1/p , for a/ b, p / − 1, p / 0, LP a, b b − a / log b − loga , for a/ b, p −1, and LP a, b 1/e b/a 1/ b−a , for a/ b, p 0. In this paper, we prove that G a, b H a, b 2L−7/2 a, b , A a, b H a, b 2L−2 a, b , and L−5 a, b H a, b for all a, b > 0, and the co...
متن کاملOn Weighted Generalized Logarithmic Means
An integral representation of Neuman is extended and used to suggest a multidimensional weighted generalized logarithmic mean. Some inequalities are established for such means. A number of known results appear as special cases.
متن کاملBest Possible Inequalities between Generalized Logarithmic Mean and Classical Means
and Applied Analysis 3 Theorem B. For all positive real numbers a and b with a/ b, we have √ G a, b A a, b < √ L a, b I a, b
متن کاملComplete Monotonicity of Logarithmic Mean
In the article, the logarithmic mean is proved to be completely monotonic and an open problem about the logarithmically complete monotonicity of the extended mean values is posed.
متن کاملOptimal Inequalities for Generalized Logarithmic, Arithmetic, and Geometric Means
Copyright q 2010 B.-Y. Long and Y.-M. Chu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. For p ∈ R, the generalized logarithmic mean L p a, b, arithmetic mean Aa, b, and geometric mean Ga, b of two positive numbers a and b are d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2007
ISSN: 1331-4343
DOI: 10.7153/mia-10-52