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NEW COINCIDENCE POINT THEOREMS IN CONTINUOUS FUNCTION SPACES AND APPLICATIONS

Part of: Nonlinear operators and their properties

Published online by Cambridge University Press:  06 July 2009

JUN WU  and
YICHENG LIU
JUN WU*
Affiliation:
College of Mathematics and Computer Science, Changsha University of Science Technology, Changsha, 410076, People’s Republic of China (email: junwmath@hotmail.com)
YICHENG LIU
Affiliation:
Department of Mathematics and System Sciences, College of Science, National University of Defense Technology, Changsha, 410073, People’s Republic of China (email: liuyc2001@hotmail.com)
*
✉For correspondence; e-mail: junwmath@hotmail.com
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Abstract

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In this paper, some new coincidence point theorems in continuous function spaces are presented. We show the hybrid mapping version and multivalued version of both Lou’s fixed point theorem (Proc. Amer. Math. Soc.127 (1999)) and de Pascale and de Pascale’s fixed point theorem (Proc. Amer. Math. Soc.130 (2002)). Our new results encompass a number of previously known generalizations of the theorems. Two examples are presented.

Keywords

fixed point theoremmultivalued mappingcoincidence point

MSC classification

Secondary: 47H10: Fixed-point theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 1 , August 2009 , pp. 26 - 37
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

The work of J. Wu has been partially supported by the Scientific Research Fund of Hunan Provincial Education Department (08C117) and the Scientific Research Fund for the Doctoral Program of CSUST (1004132).

References

[1] Covitz, H. and Nadler, S. B., ‘Multivalued contraction mappings in generalized metric spaces’, Israel J. Math. 8 (1970), 5–11.CrossRefGoogle Scholar
[2] de Pascale, E. and de Pascale, L., ‘Fixed points for some non-obviously contractive operators’, Proc. Amer. Math. Soc. 130 (2002), 3249–3254.CrossRefGoogle Scholar
[3] de Pascale, E. and Zabreiko, P. P., ‘Fixed point theorems for operators in spaces of continuous functions’, Fixed Point Theory 5 (2004), 117–129.Google Scholar
[4] Liu, Y., Wu, J. and Li, Z., ‘Common fixed points of singlevalued and multivalued maps’, Int. J. Math. Math. Sci. 19 (2005), 3045–3055.CrossRefGoogle Scholar
[5] Lou, B., ‘Fixed points for operators in a space of continuous functions and applications’, Proc. Amer. Math. Soc. 127 (1999), 2259–2264.CrossRefGoogle Scholar
[6] Suzuki, T., ‘Lou’s fixed point theorem in a space of continuous mappings’, J. Math. Soc. Japan. 58 (2006), 669–774.CrossRefGoogle Scholar