An asymptotic fixed point theorem for a locally convex space

Burton, T. A.; Dwiggins, D. P.

doi:10.1090/S0002-9939-1988-0938677-9

An asymptotic fixed point theorem for a locally convex space
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by T. A. Burton and D. P. Dwiggins PDF

Proc. Amer. Math. Soc. 103 (1988), 247-251 Request permission

Abstract:

The asymptotic fixed point theorem of Horn is extended to a locally convex topological vector space. Applications to differential equations with infinite delay are discussed.

References

O. A. Arino, T. A. Burton, and J. R. Haddock, Periodic solutions to functional-differential equations, Proc. Roy. Soc. Edinburgh Sect. A 101 (1985), no. 3-4, 253–271. MR 824225, DOI 10.1017/S0308210500020813
Felix E. Browder, On a generalization of the Schauder fixed point theorem, Duke Math. J. 26 (1959), 291–303. MR 105629
Felix E. Browder, Asymptotic fixed point theorems, Math. Ann. 185 (1970), 38–60. MR 275408, DOI 10.1007/BF01350760
T. A. Burton, Stability and periodic solutions of ordinary and functional-differential equations, Mathematics in Science and Engineering, vol. 178, Academic Press, Inc., Orlando, FL, 1985. MR 837654
T. A. Burton, Periodic solutions of nonlinear Volterra equations, Funkcial. Ekvac. 27 (1984), no. 3, 301–317. MR 794758

Periodic solutions of functional differential equations

(2) (6) IV

Jack Hale, Theory of functional differential equations, 2nd ed., Applied Mathematical Sciences, Vol. 3, Springer-Verlag, New York-Heidelberg, 1977. MR 0508721
Jack K. Hale and Orlando Lopes, Fixed point theorems and dissipative processes, J. Differential Equations 13 (1973), 391–402. MR 333851, DOI 10.1016/0022-0396(73)90025-9
W. A. Horn, Some fixed point theorems for compact maps and flows in Banach spaces, Trans. Amer. Math. Soc. 149 (1970), 391–404. MR 267432, DOI 10.1090/S0002-9947-1970-0267432-1

Continuous dependence of solutions for integrodifferential equations with infinite delay

Paul Massatt, Stability and fixed points of point-dissipative systems, J. Differential Equations 40 (1981), no. 2, 217–231. MR 619135, DOI 10.1016/0022-0396(81)90019-X

Remarks on a paper of Horn

D. R. Smart, Fixed point theorems, Cambridge Tracts in Mathematics, No. 66, Cambridge University Press, London-New York, 1974. MR 0467717
Stephen Willard, General topology, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1970. MR 0264581