Schur m -Power Convexity of a Class of Multiplicatively Convex Functions and Applications
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-20
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
We investigate the conditions under which the symmetric functions F n , k ( x , r ) = ∏ 1 ≤ i 1 < i 2 < ⋯ < i k ≤ n f ( ∑ j = 1 k x i j r ) 1 / r , k = 1,2 , … , n, are Schur m -power convex for x ∈ R + + n and r > 0 .
As a consequence, we prove that these functions are Schurgeometrically convex and Schur harmonically convex, whichgeneralizes some known results.
By applying the theory ofmajorization, several inequalities involving the p th power mean andthe arithmetic, the geometric, or the harmonic means are presented.
American Psychological Association (APA)
Wang, Wen& Yang, Shiguo. 2014. Schur m -Power Convexity of a Class of Multiplicatively Convex Functions and Applications. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-1033639
Modern Language Association (MLA)
Wang, Wen& Yang, Shiguo. Schur m -Power Convexity of a Class of Multiplicatively Convex Functions and Applications. Abstract and Applied Analysis No. 2014 (2014), pp.1-12.
https://search.emarefa.net/detail/BIM-1033639
American Medical Association (AMA)
Wang, Wen& Yang, Shiguo. Schur m -Power Convexity of a Class of Multiplicatively Convex Functions and Applications. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-1033639
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1033639