Fixed points and random fixed points for weakly inward approximable maps

O’Regan, Donal

doi:10.1090/S0002-9939-98-04601-2

Fixed points and random fixed points for weakly inward approximable maps
HTML articles powered by AMS MathViewer

by Donal O’Regan PDF

Proc. Amer. Math. Soc. 126 (1998), 3045-3053 Request permission

Abstract:

In this paper we obtain new fixed point and random fixed point theory for approximable maps.

References

Józef Banaś and Kazimierz Goebel, Measures of noncompactness in Banach spaces, Lecture Notes in Pure and Applied Mathematics, vol. 60, Marcel Dekker, Inc., New York, 1980. MR 591679
H. Ben-El-Mechaiekh and P. Deguire, Approachability and fixed points for nonconvex set-valued maps, J. Math. Anal. Appl. 170 (1992), no. 2, 477–500. MR 1188567, DOI 10.1016/0022-247X(92)90032-9
H. Ben-El-Mechaiekh and A. Idzik, A Leray-Schauder type theorem for approximable maps, Proc. Amer. Math. Soc. 122 (1994), no. 1, 105–109. MR 1212281, DOI 10.1090/S0002-9939-1994-1212281-2
Arrigo Cellina, A theorem on the approximation of compact multivalued mappings, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 47 (1969), 429–433 (1970) (English, with Italian summary). MR 276936
Klaus Deimling, Multivalued differential equations, De Gruyter Series in Nonlinear Analysis and Applications, vol. 1, Walter de Gruyter & Co., Berlin, 1992. MR 1189795, DOI 10.1515/9783110874228
P. M. Fitzpatrick and W. V. Petryshyn, Fixed point theorems for multivalued noncompact acyclic mappings, Pacific J. Math. 54 (1974), no. 2, 17–23. MR 405179, DOI 10.2140/pjm.1974.54.17
Lech Górniewicz, Andrzej Granas, and Wojciech Kryszewski, Sur la méthode de l’homotopie dans la théorie des points fixes pour les applications multivoques. I. Transversalité topologique, C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), no. 9, 489–492 (French, with English summary). MR 964113
Marc Lassonde, On the use of KKM multifunctions in fixed point theory and related topics, J. Math. Anal. Appl. 97 (1983), no. 1, 151–201. MR 721236, DOI 10.1016/0022-247X(83)90244-5
Donal O’Regan, Some fixed point theorems for concentrative mappings between locally convex linear topological spaces, Nonlinear Anal. 27 (1996), no. 12, 1437–1446. MR 1408881, DOI 10.1016/0362-546X(95)00130-N
D. O’Regan, A topological approach to integral inclusions, Proc. Royal Irish Acad., 97A (1997), 101–111.
D. O’Regan, A continuation theory for weakly inward mappings, Glasgow Math. Journal, to appear.
Sehie Park, Fixed points of approximable maps, Proc. Amer. Math. Soc. 124 (1996), no. 10, 3109–3114. MR 1343717, DOI 10.1090/S0002-9939-96-03512-5
Simeon Reich, A fixed point theorem for Fréchet spaces, J. Math. Anal. Appl. 78 (1980), no. 1, 33–35. MR 595760, DOI 10.1016/0022-247X(80)90206-1
Kok-Keong Tan and Xian-Zhi Yuan, Random fixed-point theorems and approximation in cones, J. Math. Anal. Appl. 185 (1994), no. 2, 378–390. MR 1283065, DOI 10.1006/jmaa.1994.1256