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

### From NZJM

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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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