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On some theorems of Tarafdar

Published online by Cambridge University Press:  17 April 2009

S.A. Husain  and
V.M. Sehgal
S.A. Husain
Affiliation:
Department of Mathematics, University of Wyoming, Laramie, Wyoming, USA.
V.M. Sehgal
Affiliation:
Department of Mathematics, University of Wyoming, Laramie, Wyoming, USA.
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Abstract

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In a recent paper (Bull. Austral. Math. Soc. 13 (1975), 241–245), Tarafdar has considered nonexpansive self mappings on a subset X of a locally convex vector space E and proved an extension to E of a theorem of Göhde. The purpose of this paper is to show that the condition f: X → X, in Göhde-Tarafdar's Theorem in the above paper, may be weakened to f: X → E with f(∂X) ⊆ X. As a consequence, it is further shown that an extension to E of a well-known common fixed point theorem of Belluce and Kirk due to Tarafdar remains true on domains that are not necessarily bounded or quasi-complete.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 2 , October 1976 , pp. 213 - 221
Copyright
Copyright © Australian Mathematical Society 1976

References

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