The purpose of this paper is to give new characterizations of some mean-values of two positive real numbers. The arithmetic, geometric, and harmonic means of two positive real numbers are the fundamentals of this paper.
Functional Equalities and Some Mean Values
✍ Scribed by Shoshana Abramovich; Josip Pec̆arić
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 60 KB
- Volume
- 250
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
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.
Generally, a mean value is defined as a function M: ޒ q = ޒ q ª ޒ q which satisfies the following postulate
A formula is derived from which one can obtain a family of two-sided inequali-Ž n r . 1r r ties involving the elementary mean values Ý w x . In particular, one member of this family provides a new refinement of the arithmetic mean-geometric mean inequality.