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Homotopy invariant results on complete gauge spaces

Published online by Cambridge University Press:  17 April 2009

Ravi P. Agarwal
Affiliation:
Department of Mathematical Science, Florida Institute of Technology, Melbourne, Fl 32901, United States of America
Yeol Je Cho
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland
Donal O'Regan
Affiliation:
Department of Mathematics, Gyeongsang National University, Chinju 660–701, Korea
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Abstract

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A fixed point theorem and two homotopy invariant results are presented for generalized contractive maps defined on complete gauge spaces.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Agarwal, R.P. and O'Regan, D., ‘Fixed point theory for generalized contractions on spaces with two metrics’, J. Math. Anal. Appl., 248 (2000), 402414.CrossRefGoogle Scholar
[2]Agarwal, R.P. and O'Regan, D., ‘Fixed point theorems for multivalued maps with closed values in complete gauge spaces’, Appl. Math. Lett. 14 (2001), 831836.Google Scholar
[3]Cain, G.L. and Nashed, M.Z., ‘Fixed points and stability for the sum of two operators in locally convex spaces’, Pacific J. Math. 39 (1971), 581592.Google Scholar
[4]Dugundji, J., Topology (Ally and Bacon, Boston, 1966).Google Scholar
[5]Frigon, M., ‘On continuation methods for contractive and nonexpansive mappings’, in Recent advances in metric fixed point theory, Sevilla 1995, (Benavides, T. Dominguez, Editor), Ciencias 48 (Universidad de Sevilla, Sevilla, 1996), pp. 1930.Google Scholar
[6]Frigon, M., Fixed point results for multivalued contractions on gauge spaces, (Agarwal, R.P. and O'Regan, D., Editors), Set Valued Mappings with Applications in Nonlinear Analysis (Gordon and Breach Publishers, to appear).Google Scholar
[7]O'Regan, D., ‘Fixed point theorems for nonlinear operators’, J. Math. Anal. Appl. 202 (1996), 413432.Google Scholar
[8]O'Regan, D. and Precup, R., Theorems of Leray-Schauder type and applications (Gordon and Breach, Amsterdam, 2001).Google Scholar
[9]Sims, B., Xu, H.K. and Yuan, G.X.Z., ‘The homotopic invariance for fixed points of set-valued nonexpansive mappings‘, in Fixed Point Theory and Applocations 2, (Cho, Y.J., Kim, J.K. and Kang, S.M., Editors) (Nova Science Publishers, Huntington, 2001), pp. 93104.Google Scholar