Abstract
Geometric and harmonic means of two convex functionals have been recently constructed. The aim of this work is to study the stability of these operations. The development of this theory is very useful in many contexts. The obtained results generalize the case of symmetric positive operators which have been studied in the literature.
References
- M. Atteia, M. Raïssouli: Self dual operators on convex functionals, geometric mean and square root of convex functionals, J. Conv. Anal. 8(1) (2001) 223–240.https://doi.org/10.68381/jca08010Google Scholar
- H. Attouch: Variational Convergence for Functions and Operators, Pitman, Boston, London (1984).Google Scholar
- T. Ando: Topics on Operators Inequalities, Ryukuyu Univ. Lecture Note Series 1 (1978).Google Scholar
- N. Anderson Jr., R. J. Duffin: Series and parallel addition of matrices, J. Math. Anal. Appl. 26 (1969) 576–594.https://doi.org/10.1016/0022-247X(69)90200-5Google Scholar
- G. Beer: Topologies on closed and closed convex sets, Department of Mathematics and Computer Science, California State University, Los Angeles (1993).https://doi.org/10.1007/978-94-015-8149-3Google Scholar
- R. Bergstrom, L. Mc Linden: Preservation of convergence of convex sets and functions in finite dimensions, Trans. Amer. Math. Soc. 268 (1981) 127–142.https://doi.org/10.1090/S0002-9947-1981-0628449-5Google Scholar
- M. Chergui: Logarithme d’un Opéreateur, Moyenne Géométrique de Deux Opérateurs Nonbornés, Etude des Propriétés Algébriques et Topologiques, Thèse de 3ème cycle, Université Moulay Ismaïl, Faculté des Sciences de Meknes, (1999).Google Scholar
- J. Fujii, M. Fujii: On geometric and harmonic means of positive operators, Math Japonica 24(2) (1979) 203–207.Google Scholar
- J. Fujii: Arithmetico-geometric mean of operators, Math Japonica 23 (1978) 667–669.Google Scholar
- J. B. Hiriart-Urruty, C. Lemarechal: Convex Analysis and Minimization Algorithms, Grundlehren der Mathematischen Wissenschaften 305, 306, Springer-Verlag (1993).https://doi.org/10.1007/978-3-662-02796-7Google Scholar
- E. Idee: Minimisation d’une Fonction Quasi-Convexe Aléatoire: Application, Thèse Grenoble, France (1973).Google Scholar
- J. J. Moreau: Fonctionnelles Convexes, Séminaire sur les équations aux dérivées partielles II, Collège de France (1966-1967).Google Scholar
- M. Raïssouli, M. Chergui: Arithmetico-geometric and geometrico-harmonic means of two convex functionals, Scientiae Mathematicae Japonicae 55(3) (2002) 485–492.Google Scholar
- R. T. Rockafellar: Convex Analysis, Princeton University Press, Princeton, N.J. (1970).Google Scholar
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Published by Heldermann Verlag, 2003. Rights now held by Banach Press LLC.
