The Optimal Upper and Lower Power Mean Bounds for a Convex Combination of the Arithmetic and Logarithmic Means
Joint Authors
Xia, Wei-Feng
Chu, Yu-Ming
Wang, Gen-Di
Source
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-04-19
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
For p∈ℝ, the power mean Mp(a,b) of order p, logarithmic mean L(a,b), and arithmetic mean A(a,b) of two positive real values a and b are defined by Mp(a,b)=((ap+bp)/2)1/p, for p≠0 and Mp(a,b)=ab, for p=0, L(a,b)=(b-a)/(logb-loga), for a≠b and L(a,b)=a, for a=b and A(a,b)=(a+b)/2, respectively.
In this paper, we answer the question: for α∈(0,1), what are the greatest value p and the least value q, such that the double inequality Mp(a,b)≤αA(a,b)+(1-α)L(a,b)≤Mq(a,b) holds for all a,b>0?
American Psychological Association (APA)
Xia, Wei-Feng& Chu, Yu-Ming& Wang, Gen-Di. 2010. The Optimal Upper and Lower Power Mean Bounds for a Convex Combination of the Arithmetic and Logarithmic Means. Abstract and Applied Analysis،Vol. 2010, no. 2010, pp.1-9.
https://search.emarefa.net/detail/BIM-484424
Modern Language Association (MLA)
Xia, Wei-Feng…[et al.]. The Optimal Upper and Lower Power Mean Bounds for a Convex Combination of the Arithmetic and Logarithmic Means. Abstract and Applied Analysis No. 2010 (2010), pp.1-9.
https://search.emarefa.net/detail/BIM-484424
American Medical Association (AMA)
Xia, Wei-Feng& Chu, Yu-Ming& Wang, Gen-Di. The Optimal Upper and Lower Power Mean Bounds for a Convex Combination of the Arithmetic and Logarithmic Means. Abstract and Applied Analysis. 2010. Vol. 2010, no. 2010, pp.1-9.
https://search.emarefa.net/detail/BIM-484424
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-484424