A Geometric Mean of Parameterized Arithmetic and Harmonic Means of Convex Functions. (30th December 2012)

• Record Type: Journal Article
• Authors: Kum, Sangho; Lim, Yongdo
• Other Names: Lee Gue Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-12-30
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/836804
• Languages: English
• ISSNs: 1085-3375

Abstract

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.