Abstract
The continuation theorem for contractive mappings on spaces endowed with two metrics is used to obtain existence, uniqueness and iterative approximation results for nonlinear integral equations in Banach spaces.
Authors
Radu Precup
Babeș-Bolyai University
Babeș-Bolyai University
Keywords
??
Cite this paper as:
R. Precup, Discrete continuation method for nonlinear integral equations in Banach spaces, Pure Math. Appl., 11 (2000), 375-384.
About this paper
Journal
Pure Mathematics and Applications
Publisher Name
PU.M.A.
DOI
??
Print ISSN
Not available yet.
Online ISSN
Not available yet.
Google Scholar Profile
References
[1] C. CORDUNEANU, Integral Equations and Applications, Cambridge Univ. Press, New York, 1991.
[2] A. GRANAS, Continuation method for contractive maps, Topol. Methods Nonlinear Anal. 3(1994), 375-379.
[3] A. GRANAS, R. B. GUENTHER, J. W. LEE, Some general existence principles in the Caratheodory theory of nonlinear differential systems, J. Math. Pures et Appl. 70 (1991), 153-196.
[4] M.A. KRASNOSELSKII, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, Oxford, 1964.
[5] M.O. MOORE, Computational Functional Analysis, Halsted Press, New York, 1985.
[6] D. O’REGAN, Volterra and Urysohn integral equations in Banach spaces, J. Appl. Math. Stochastic Anal. 11 (1998), 449-464.
[7] R. PRECUP, Nonlinear Integral Equations (Romanian), ”Babes-Bolyai” Univ., Cluj, 1993.
[8] R. PRECUP, Existence theorems for nonlinear problems by continuation methods, Nonlinear Anal. 30 (1997), no. 6, 3313-3322.
[9] R. PRECUP, Discrete continuation method for boundary value problems on bounded sets in Banach spaces, J. Comput. Appl. Math. 113 (2000), 267-281.
[10] K. YOSIDA, Functional Analysis, Springer-Verlag, Berlin, 1978