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Fixed points for operators in a space of continuous functions and applications

Author(s): Bendong Lou
Journal: Proc. Amer. Math. Soc. 127 (1999), 2259-2264.
MSC (1991): Primary 47H10
Posted: April 8, 1999
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Abstract: This paper investigates the fixed points for self-maps of a closed set in a space of abstract continuous functions. Our main results essentially extend the Banach contracting mapping principle. An application to integro-differential equations is given.

References:

1.: E. C. Titchmarsh, The Theory of the Riemann-Zeta-function, Second Edition, Clarendon Press, Oxford, 1986. MR 88c:11049
2.: L. H. Erbe and Dajun Guo, Periodic boundary value problems for second order integrodifferential equations of mixed type, Appl. Anal., 46 (1992), 249-258. MR 93f:34119
3.: Jingxian Sun and Zengqin Zhao, Extremal solutions of initial value problem for integro-differential equations of mixed type in Banach spaces, Ann. of Diff. Eqs., 8 (1992), 469-475. (CHINA). MR 94c:45012

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Additional Information:

Bendong Lou
Affiliation: Department of Mathematics, Shandong University, Jinan 250100, People's Republic of China
Email: blou@math.sdu.edu.cn

DOI: 10.1090/S0002-9939-99-05211-9
PII: S 0002-9939(99)05211-9
Keywords: Fixed point, self-maps of a closed set, iterative sequence
Received by editor(s): October 10, 1997
Posted: April 8, 1999
Additional Notes: The author is supported by the National Natural Science Foundation of China and the State Education Commission Doctoral Foundation of China.
Communicated by: David R. Larson
Copyright of article: Copyright 1999, American Mathematical Society


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