An Effective Metric on C(H,K) with Normal Structure


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New Zealand Journal of Mathematics

Vol. 46, (2016), Pages 53-64

Mona Nabiei

Department of Mathematics

Shahid Beheshti University, G. C.

P.o. Box 19839

Tehran, Iran.

Abstract This study first defines a new metric with normal structure on C(H,K) and then a new technique to prove fixed point theorems for families of non-expansive maps on this metric space. Indeed, it shows that the presence of a bounded orbit implies the existence of a fixed point for a group of h-biholomorphic automorphisms on C(H,K).

Keywords Closed operator, Fixed point, h-biholomorphic, Metrically convex, Normal structure.

Classification (MSC2000) 47L60, 47B38, 54E99.

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