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Results on common fixed points on complete metric spaces

Published online by Cambridge University Press:  18 May 2009

Brian Fisher
Brian Fisher
Affiliation:
Department of Mathematics, The University, Leicester LE1 7RH
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The following theorem was proved in [1].

Theorem 1. Let S and T be continuous, commuting mappings of a complete, bounded metric space (X, d) into itself satisfying the inequality

for all x, y in X, where 0≤c<1 and p, p′, q, q′≥0 are fixed integers with p+p′, q+q′≥1. Then S and T have a unique common fixed point z. Further, if p′ or q′ = 0, then z is the unique fixed point of S and if p or q = 0, then z is the unique fixed point of T.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 21 , Issue 1 , January 1980 , pp. 165 - 167
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

REFERENCE

1.Fisher, B., Results on common fixed points on bounded metric spaces, Math. Sem. Notes Kobe Univ., 7 (1979), 73–80.Google Scholar