SUMS OF HOLOMORPHIC SELFMAPS OF THE UNIT DISK II by

SUMS OF HOLOMORPHIC SELFMAPS OF THE UNIT DISK II by

SUMS OF HOLOMORPHIC SELFMAPS
OF THE UNIT DISK II
by
Raymond Mortini & Georges Rhin
˛Abstract.
` —
´ ˛ We confirm a conjecture in [1, p. 110] by showing that
˛ 1+z + 1−z p ˛ ≤ 1 for all p ≥ 1 and z in the closed unit disk D.
2
2
References
[1] R. Mortini, R. Rupp. Sums of holomorphic selfmaps of the unit disk, Annales
Univ. Mariae Curie-Sklodowska 61 (2007), 107-115.
Raymond Mortini, Département de Mathématiques, LMAM, UMR 7122, Uni-
versité Paul Verlaine, Ile du Saulcy, F-57045 Metz, France
E-mail : [email protected]
Georges Rhin, Département de Mathématiques, LMAM, UMR 7122, Université Paul Verlaine, Ile du Saulcy, F-57045 Metz, France
E-mail : [email protected]
2010 Mathematics Subject Classification. — Primary 30A10; Secondary 26D05; 30J99.
Key words and phrases. — selfmaps; unit disk; inequalities; trigonometric functions.