A Geometric Mean of Parameterized Arithmetic and Harmonic Means of Convex Functions

Sangho Kum and Yongdo Lim

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: The notion of the geometric mean of two positive reals is extended by Ando (1978) to the case of positive semidefinite matrices A and B. Moreover, an interesting generalization of the geometric mean A # B of A and B to convex functions was introduced by Atteia and Raïssouli (2001) with a different viewpoint of convex analysis. The present work aims at providing a further development of the geometric mean of convex functions due to Atteia and Raïssouli (2001). A new algorithmic self‐dual operator for convex functions named “the geometric mean of parameterized arithmetic and harmonic means of convex functions” is proposed, and its essential properties are investigated.

Date: 2012
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https://doi.org/10.1155/2012/836804

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:836804

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