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On triangle contractive operators in Hilbert spaces

Published online by Cambridge University Press:  24 October 2008

Dang Dinh Ang  and
Le Hoan Hoa
Dang Dinh Ang
Affiliation:
University, Ho Chi Minh City, Vietnam
Le Hoan Hoa
Affiliation:
University, Ho Chi Minh City, Vietnam
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Abstract

Let H be a finite dimensional real or complex Hilbert space. We denote by Λ(x, y, z) the area of the triangle with vertices x, y, z ∈ H. A map f: H → H is triangle contractive TC if 0 < α < 1 and for each x, y, z ∈ H either

or

and

and

We prove that if f is TC either there is a fixed point w = f(w) or a fixed line L = ⊃ f(L) We characterize the f which are TC and continuous but have no fixed point.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 1 , January 1979 , pp. 17 - 20
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

REFERENCES

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