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

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  • Sangho Kum
  • Yongdo Lim

Abstract

The notion of the geometric mean of two positive reals is extended by Ando (1978) to the case of positive semidefinite matrices and . Moreover, an interesting generalization of the geometric mean of and 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.

Suggested Citation

  • Sangho Kum & Yongdo Lim, 2012. "A Geometric Mean of Parameterized Arithmetic and Harmonic Means of Convex Functions," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, December.
    • Handle: RePEc:hin:jnlaaa:836804
    DOI: 10.1155/2012/836804
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    Cited by:

    1. Troon, Benedict, 2021. "Estimation Of Variation About The Mean Using Geometric Measure," AfricArxiv jtn64, Center for Open Science.

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