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Common fixed point theorems for two mappings satisfying some conditions

Published online by Cambridge University Press:  17 April 2009

Jeong Sheok Ume  and
Jong Kyu Kim
Jeong Sheok Ume
Affiliation:
Department of Applied Mathematics, Changwon National UniversityChangwon 641–773, Korea e-mail: jsume@sarim.changwon.ac.kr
Jong Kyu Kim
Affiliation:
Department of Mathematics, Kyungnam University, Masan 631–701,Korea e-mail: jongkyuk@hanma.kyungnam.ac.kr
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Abstract

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In this paper, using the concept of w-distance, we first prove common fixed point theorems in a complete metric space. Then these theorems are used to improve Kannan's fixed point theorem, Ćirić's fixed point theorem, Kada, Suzuki and Takahashi's fixed point theorem and Ume's fixed point theorem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 1 , August 2000 , pp. 75 - 85
Copyright
Copyright © Australian Mathematical Society 2000

References

1Ćirić, L.J., ‘A generalization of Banach's contraction principle’, Proc. Amer. Math. Soc. 45 (1974), 267–273.Google Scholar
2Kada, O., Suzuki, T. and Takahashi, W., ‘Nonconvex minimization theorems and fixed point theorems in complete metric spaces’, Math. Japon. 44 (1996), 381–391.Google Scholar
3Kannan, R., ‘Some results on fixed points-II’, Amer. Math. Monthly 76 (1969), 405–408.Google Scholar
4Ume, J.S., ‘Fixed point theorems related to Ćirić's contraction principle’, J. Math. Anal. Appl. 225 (1998), 630–640.CrossRefGoogle Scholar