Fixed point theorems in product spaces
HTML articles powered by AMS MathViewer
- by Tadeusz Kuczumow PDF
- Proc. Amer. Math. Soc. 108 (1990), 727-729 Request permission
Abstract:
If ${K_1}$ and ${K_2}$ are nonempty closed weakly compact subsets of Banach spaces and they have the generic fixed point property for nonexpansive mappings, then in the maximum norm ${K_1} \times {K_2}$ has fixed point property for nonexpansive mappings.References
- Ronald E. Bruck Jr., Properties of fixed-point sets of nonexpansive mappings in Banach spaces, Trans. Amer. Math. Soc. 179 (1973), 251–262. MR 324491, DOI 10.1090/S0002-9947-1973-0324491-8
- Ali A. Fora, A fixed point theorem for product spaces, Pacific J. Math. 99 (1982), no. 2, 327–335. MR 658063
- W. A. Kirk, Fixed point theory for nonexpansive mappings, Fixed point theory (Sherbrooke, Que., 1980) Lecture Notes in Math., vol. 886, Springer, Berlin-New York, 1981, pp. 484–505. MR 643024
- W. A. Kirk, Fixed point theory for nonexpansive mappings. II, Fixed points and nonexpansive mappings (Cincinnati, Ohio, 1982) Contemp. Math., vol. 18, Amer. Math. Soc., Providence, RI, 1983, pp. 121–140. MR 728596, DOI 10.1090/conm/018/728596
- W. A. Kirk, Nonexpansive mappings in product spaces, set-valued mappings and $k$-uniform rotundity, Nonlinear functional analysis and its applications, Part 2 (Berkeley, Calif., 1983) Proc. Sympos. Pure Math., vol. 45, Amer. Math. Soc., Providence, RI, 1986, pp. 51–64. MR 843594 —, Fixed points theorems in product spaces, Operator Equations and Fixed Points (S. P. Singh, V. M. Seghal, and J. H. W. Burry, eds.), Math. Sci. Res. Inst. Korea 1 (1986), 27-35.
- W. A. Kirk, An iteration process for nonexpansive mappings with applications to fixed point theory in product spaces, Proc. Amer. Math. Soc. 107 (1989), no. 2, 411–415. MR 941325, DOI 10.1090/S0002-9939-1989-0941325-6
- W. A. Kirk and Carlos Martínez-Yañez, Nonexpansive and locally nonexpansive mappings in product spaces, Nonlinear Anal. 12 (1988), no. 7, 719–725. MR 947884, DOI 10.1016/0362-546X(88)90024-7
- W. A. Kirk and Y. Sternfeld, The fixed point property for nonexpansive mappings in certain product spaces, Houston J. Math. 10 (1984), no. 2, 207–214. MR 744905
- Sam B. Nadler Jr., Sequences of contractions and fixed points, Pacific J. Math. 27 (1968), 579–585. MR 240802 —, The fixed point property for nonexpansive mappings II, Amer. Math. Monthly 87 (1980), 292-294.
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 727-729
- MSC: Primary 47H10; Secondary 47H09
- DOI: https://doi.org/10.1090/S0002-9939-1990-0991700-7
- MathSciNet review: 991700