Generally, a mean value is defined as a function M: β«ήβ¬ q = β«ήβ¬ q Βͺ β«ήβ¬ q which satisfies the following postulate
Some Mean Values Related to the Quasi-Arithmetic Mean
β Scribed by Jeong Sheok Ume; Young-Ho Kim
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 77 KB
- Volume
- 252
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
β¦ Synopsis
In this article, we study new mean values and their properties related to the quasi-arithmetic mean and their properties in the spirit of H. Haruki and Th. M. Rassias.
π SIMILAR VOLUMES
Let , , β₯ , β€ : 0, Ο± Βͺ R, strictly monotonic and continuous functions, be the generators of the positively homogeneous quasi-arithmetic means M , M , M , β₯ and M . The main result gives full characterizations of the functions , , β₯ , and β€ β€ such that M M x, y , M x, y sM x, y , x, y)0.
Let a(n) be an arithmetical function satisfying some conditions and write $ n x a(n)=main term+E(x). We obtain an asymptotic formula for a weighted mean square of the error term for some constants \_ 0 and c, by modifying a method that seems due to Titchmarsh. This method utilizes the following too
Two recent investigations have sssessed the role of altered affective states in relation to suicide. Spiegel and Neuringer(6) found that suicide note writers who subsequently committed suicide were far less explicit about their suicidal intentions than those who faked suicide notes. It appeared that