Domain invariance theorems for contractive type maps


New domain invariance theorems are presented for nonlinear contractions on spaces with two metrics.


Bavi P. Agarwal
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901–6975

Donal O’Regan
Department of Mathematics, National University of Ireland, Galway, Ireland

Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


Domain invariance; nonlinear contractions; two metrics.

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R.P. Agarwal, D. O’Regan, R. Precup, Domain invariance theorems for contractive type maps, Dynamic Systems Appl. 16 (3) (2007), 579-586.


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Dynamic Systems and Applications

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[1] R.P. Agarwal, Y.J. Cho and D. O’Regan, Homotopy type results for nonlinear contractive spaces with two metrics, to appear in Proc. 7th International Conference on Nonlinear Functional Analysis and Applications, Korea, 2001, Nova Science Publishers, New York.
[2] D.W. Boyd and J.S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20(1969), 458–464.
[3] J. Dugundji and A. Granas, Fixed point theory, Monografie Matematyczne, Vol 16, Polish Scientific Publishers, 1982.
[4] K. Goebel and W.A. Kirk, Topics in metric fixed point theory, Cambridge University Press, 1990.
[5] D. O’Regan and R. Precup, Theorems of Leray–Schauder type and applications, Gordon and Breach Publishers, Amsterdam, 2001.
[6] R. Precup, Discrete continuation method for boundary value problems on bounded sets in Banach spaces, J. Comput. Appl. Math. 113(2000), 267–281.


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