Abstract
Two continuation methods are described in this paper. The first is based on essential mapswhereas the second is based on 0-epi maps.
Similar content being viewed by others
References
Aliprantis, C. D. and Border, K. C.: Infinite Dimensional Analysis, Springer-Verlag, Berlin, 1994.
Fitzpatrick, P. M. and Petryshyn, W. V.: Fixed point theorems for multivalued noncompact acyclic mappings,Pacific J. Math. 54 (1974), 17–23.
Furi, M., Martelli, M., and Vignoli, A.: On the solvability of nonlinear operator equations in normed spaces,Ann. Math. Pura Appl. 124 (1980), 321–343.
Gorniewicz, L.: Homological methods in fixed point theory of multivalued mappings,Dissertationes Math. 129 (1976), 1–71.
Gorniewicz, L., Granas, A., and Kryszewski, W.: Sur laméthode de d’homotopie dans la théorie des points fixes. Partie 1: Transversalité topologique,C.R. Acad. Sci. Paris 307 (1988), 489–492.
Gorniewicz, L. and Slosarski, M.: Topological essentiality and differential inclusions,Bull. Austral. Math. Soc. 45 (1992), 177–193.
Granas, A.: Sur la méthode de continuité de Poincaré,C.R. Acad. Sci. Paris 282 (1976), 983–985.
O’Regan, D.: Some fixed point theorems for concentrative mappings between locally convex spaces,Nonlinear Anal. 27 (1996), 1437–1446.
O’Regan, D.: Continuation fixed point theorems for locally convex linear topological spaces,Math. Comput. Modelling 24 (1996), 57–70.
O’Regan, D.: Fixed points for set valued mappings in locally convex linear topological spaces,Math. Comput. Modelling 28 (1998), 45–55.
O’Regan, D.: Coincidences for admissible and Ф⋆ maps,J. Math. Anal. Appl. 220 (1998), 322–333.
Petryshyn, W. V. and Fitzpatrick, P. M.: A degree theory, fixed point theorems, and mappings theorems for multivalued noncompact mappings,Trans. Amer. Math. Soc. 194 (1974), 1–25.
Su, C. H. and Sehgal, V. M.: Some fixed point theorems for condensing multifunctions in locally convex spaces,Proc. Amer. Math. Soc. 50 (1975), 150–154.
Zeidler, E.: Nonlinear Functional Analysis and its Applications, Vol. 1, Springer-Verlag, New York, 1986.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
O’Regan, D. Continuation Methods Based on Essential and 0-epi Maps. Acta Applicandae Mathematicae 54, 319–330 (1998). https://doi.org/10.1023/A:1006189718645
Issue Date:
DOI: https://doi.org/10.1023/A:1006189718645