New Characterizations of Some Mean-Values
β Scribed by Hiroshi Haruki; Themistocles M. Rassias
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 152 KB
- Volume
- 202
- Category
- Article
- ISSN
- 0022-247X
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β¦ Synopsis
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.
π SIMILAR VOLUMES
A formula is derived from which one can obtain a family of two-sided inequali-Ε½ n r . 1r r ties involving the elementary mean values Γ w x . In particular, one member of this family provides a new refinement of the arithmetic mean-geometric mean inequality.
## Abstract Let __X__ be a space of homogeneous type. The authors introduce some generalized approximations to the identity (for short, GAI) with optimal decay conditions in the sense that these conditions are the sufficient and necessary conditions for these GAI's to characterize BMO(__X__), the s
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: β«ήβ¬ q = β«ήβ¬ q Βͺ β«ήβ¬ q which satisfies the following postulate