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Common fixed points of commuting holomorphic maps

✍ Scribed by Marco Abate


Publisher
Springer
Year
1989
Tongue
English
Weight
561 KB
Volume
283
Category
Article
ISSN
0025-5831

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πŸ“œ SIMILAR VOLUMES


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Let F and G be two holomorphic maps of the unit polydisc for i=1, ..., n] which are continuous on the closure 2 n of 2 n . According to A. L. Shields [17] (for n=1), D. J. Eustice [4] (for n=2) and L. F. Heath and T. J. Suffridge [8] (for any finite n 1), if F and G commute under composition, they

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## If B n H is a Cartesian product of n Hilbert balls and F is a family of commuting holomorphic self-mappings of B n H with a nonempty common ΓΏxed point set Fix(F), then the set Fix(F) is a holomorphic retract of B n H .

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The concept of a 2-metric space, introduced by S. GAHLER [l], provides a natural abstraction of the area function for EnoLIDean triangles. Recently, KHAN and FISHER [2] have introduced a necessary and sufficient condition which guarantees the existence of a common fixed point for a pair of continuo