A new fixed point theorem on demicompact $1$-set-contraction mappings
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- by Guo Zhen Li
- Proc. Amer. Math. Soc. 97 (1986), 277-280
- DOI: https://doi.org/10.1090/S0002-9939-1986-0835880-1
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Abstract:
W. V. Petryshyn studied the fixed point theorem of demi-compact mappings. This paper gives a new fixed point theorem of demi-compact $1$-set-contraction mappings in the norm form.References
- W. V. Petryshyn, Fixed point theorems for various classes of $1$-set-contractive and $1$-ball-contractive mappings in Banach spaces, Trans. Amer. Math. Soc. 182 (1973), 323–352. MR 328688, DOI 10.1090/S0002-9947-1973-0328688-2
- W. V. Petryshyn, Construction of fixed points of demicompact mappings in Hilbert space, J. Math. Anal. Appl. 14 (1966), 276–284. MR 194942, DOI 10.1016/0022-247X(66)90027-8
- A. J. B. Potter, A fixed point theorem for positive $k$-set contractions, Proc. Edinburgh Math. Soc. (2) 19 (1974/75), 93–102. MR 380544, DOI 10.1017/S001309150001542X
- Roger D. Nussbaum, Periodic solutions of some nonlinear, autonomous functional differential equations. II, J. Differential Equations 14 (1973), 360–394. MR 372370, DOI 10.1016/0022-0396(73)90053-3
- P. M. Fitzpatrick and W. V. Petryshyn, Fixed point theorems and the fixed point index for multivalued mappings in cones, J. London Math. Soc. (2) 12 (1975/76), no. 1, 75–85. MR 405180, DOI 10.1112/jlms/s2-12.1.75
- Nguyên Phuong Các and Juan A. Gatica, Fixed point theorems for mappings in ordered Banach spaces, J. Math. Anal. Appl. 71 (1979), no. 2, 547–557. MR 548782, DOI 10.1016/0022-247X(79)90208-7
- M. A. Krasnosel′skiĭ, Positive solutions of operator equations, P. Noordhoff Ltd., Groningen, 1964. Translated from the Russian by Richard E. Flaherty; edited by Leo F. Boron. MR 0181881
Bibliographic Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 97 (1986), 277-280
- MSC: Primary 47H10; Secondary 47H09
- DOI: https://doi.org/10.1090/S0002-9939-1986-0835880-1
- MathSciNet review: 835880