Application of Liapunov’s direct method to fixed point theorems
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- by J. H. George, V. M. Sehgal and R. E. Smithson PDF
- Proc. Amer. Math. Soc. 28 (1971), 613-620 Request permission
Abstract:
The direct method of Liapunov is applied to the existence of fixed points for multivalued functions. Many recent fixed point theorems are shown to be special cases of the Liapunov theory.References
- L. P. Belluce and W. A. Kirk, Fixed-point theorems for certain classes of nonexpansive mappings, Proc. Amer. Math. Soc. 20 (1969), 141–146. MR 233341, DOI 10.1090/S0002-9939-1969-0233341-4
- F. E. Browder and W. V. Petryshyn, The solution by iteration of linear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 566–570. MR 190744, DOI 10.1090/S0002-9904-1966-11543-4
- J. B. Diaz and F. T. Metcalf, On the structure of the set of subsequential limit points of successive approximations, Bull. Amer. Math. Soc. 73 (1967), 516–519. MR 211387, DOI 10.1090/S0002-9904-1967-11725-7
- M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc. 37 (1962), 74–79. MR 133102, DOI 10.1112/jlms/s1-37.1.74
- Sam B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475–488. MR 254828, DOI 10.2140/pjm.1969.30.475
- Raymond E. Smithson, Some general properties of multi-valued functions, Pacific J. Math. 15 (1965), 681–703. MR 182955, DOI 10.2140/pjm.1965.15.681 —, A note on $M$-isometrics and contractive multifunctions, Notices Amer. Math. Soc. 17 (1970), 222. Abstract #672-486.
- Wayman L. Strother, Continuous multi-valued functions, Bol. Soc. Mat. São Paulo 10 (1955), 87–120 (1958). MR 122961
- Taro Yoshizawa, Stability theory by Liapunov’s second method, Publications of the Mathematical Society of Japan, vol. 9, Mathematical Society of Japan, Tokyo, 1966. MR 0208086
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 613-620
- MSC: Primary 54.85
- DOI: https://doi.org/10.1090/S0002-9939-1971-0281185-9
- MathSciNet review: 0281185