Data dependence of fixed points for non-self generalized contractions


Data dependence of fixed points for several classes of non-self generalized contractions is studied. A fibre non-self contraction theorem is also established. An application
to functional equations is included.


Adela Chis-Novac
Department of Mathematics, Technical University of Cluj-Napoca, Romania

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

Ioan A Rus
Department of Applied Mathematics, Babes-Bolyai University of Cluj-Napoca, Romania


Fixed point; generalized contraction; non-self operator; data dependence.

Paper coordinates

A. Chis-Novac, R. Precup,  I.A. Rus, Data dependence of fixed points for non-self generalized contractions, Fixed Point Theory 10 (2009) no.1, 73-87.


About this paper


Fixed Point Theory

Publisher Name
Print ISSN


Online ISSN


google scholar link

[1] A. Chi¸s, Fixed point theorems for generalized contractions, Fixed Point Theory, 4(2003), no.1, 33-48.
[2] A. Chi¸s and R. Precup, Continuation theory for general contractions in gauge spaces, Fixed Point Theory Appl., 3(2004), 173-185.
[3] M. Frigon, On continuation methods for contractive and nonexpansive mappings, Recent Advances on Metric Fixed Point Theory, Sevilla 1996, 19-30.
[4] M. Frigon, Fixed point and continuation results for contractions in metric and gauge spaces Fixed Point Theory and its Applications, Banach Center Publications, Warzsawa, 2007, 89-114.
[5] M. Frigon et A. Granas, Resultats du type de Leray-Schauder pour des contractions multivoques, Topol. Methods Nonlinear Anal., 4(1994), 197-208.
[6] M. Frigon et A. Granas, Resultats du type de Leray-Schauder pour des contractions sur des espaces de Fr´echet, Ann. Sci. Math. Qu´ebec, 22(1998), 161-168.
[7] M. Frechet, Les espaces abstraits, Gauthier-Villars, Paris, 1928.
[8] A. Granas, Continuation method for contractive maps, Topological Methods Nonlinear Anal., 3(1994), 375-379.
[9] M.W. Hirsch and C. C. Pugh, Stable manifolds anf hyperbolic sets, Proc. Symp. in Pure Math., Amer. Math. Soc., 14(1970), 133-143.
[10] W.A. Kirk and B. Sims (eds.), Handbook of Metric Fixed Point Theory, Kluwer, Boston, 2001.
[11] J. Matkowski, Integrable solutions of functional equations, Dissert. Math. 77, Warszawa, 1975.
[12] D. O’Regan and R. Precup, Theorems of Leray-Schauder Type and Applications, Gordon and Breach, Amsterdam, 2001.
[13] D. O’Regan and R. Precup, Continuation theory for contractions on spaces with two vector-valued metrics, Applicable Analysis, 82(2003), 131-144.
[14] D. O’Regan and R. Precup, Existence theory for nonlinear operator equations of Hammerstein type in Banach spaces, Dynamic Systems Appl., 14(2005), 121-134.
[15] R. Precup, Discrete continuation method for boundary value problems on bounded sets in Banach spaces, J. Comput. Appl. Math., 113(2000), 267-281.
[16] R. Precup, Continuation results for mappings of contractive type, Seminar on Fixed Point Theory 2(2001), 23-40.
[17] R. Precup, The continuation principle for generalized contractions, Bull. Appl. Comput. Math. (Budapest), 96(2001), 367-373.
[18] R. Precup, Methods in Nonlinear Integral Equations, Kluwer, Dordrecht-BostonLondon, 2002.

Related Posts