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Best Possible Bounds for Yang Mean Using Generalized Logarithmic Mean
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-04-10
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
We prove that the double inequality L p ( a , b ) < U ( a , b ) < L q ( a , b ) holds for all a , b > 0 with a ≠ b if and only if p ≤ p 0 and q ≥ 2 and find several sharp inequalities involving the trigonometric, hyperbolic, and inverse trigonometric functions, where p 0 = 0.5451 ⋯ is the unique solution of the equation ( p + 1 ) 1 / p = 2 π / 2 on the interval ( 0 , ∞ ) , U ( a , b ) = ( a - b ) / [ 2 arctan ( ( a - b ) / 2 a b ) ] , and L p ( a , b ) = [ ( a p + 1 - b p + 1 ) / ( ( p + 1 ) ( a - b ) ) ] 1 / p ( p ≠ - 1,0 ) , L - 1 ( a , b ) = ( a - b ) / ( log a - log b ) and L 0 ( a , b ) = ( a a / b b ) 1 / ( a - b ) / e are the Yang, and p th generalized logarithmic means of a and b , respectively.
American Psychological Association (APA)
Qian, Wei-Mao& Chu, Yu-Ming. 2016. Best Possible Bounds for Yang Mean Using Generalized Logarithmic Mean. Mathematical Problems in Engineering،Vol. 2016, no. 2016, pp.1-7.
https://search.emarefa.net/detail/BIM-1112763
Modern Language Association (MLA)
Qian, Wei-Mao& Chu, Yu-Ming. Best Possible Bounds for Yang Mean Using Generalized Logarithmic Mean. Mathematical Problems in Engineering No. 2016 (2016), pp.1-7.
https://search.emarefa.net/detail/BIM-1112763
American Medical Association (AMA)
Qian, Wei-Mao& Chu, Yu-Ming. Best Possible Bounds for Yang Mean Using Generalized Logarithmic Mean. Mathematical Problems in Engineering. 2016. Vol. 2016, no. 2016, pp.1-7.
https://search.emarefa.net/detail/BIM-1112763
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1112763