An asymptotic fixed point theorem for a locally convex space

Authors:
T. A. Burton and D. P. Dwiggins

Journal:
Proc. Amer. Math. Soc. **103** (1988), 247-251

MSC:
Primary 47H10; Secondary 54H25

DOI:
https://doi.org/10.1090/S0002-9939-1988-0938677-9

MathSciNet review:
938677

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

**[1]**O. Arino, T. A. Burton, and J. Haddock,*Periodic solutions of functional differential equations*, Proc. Roy. Soc. Edinburgh Sect. A**101A**(1985), 253-271. MR**824225 (87f:34081)****[2]**F. E. Browder,*On a generalization of the Schauder fixed point theorem*, Duke Math. J.**26**(1959), 291-303. MR**0105629 (21:4368)****[3]**-,*Asymptotic fixed point theorems*, Math. Ann.**185**(1970), 38-60. MR**0275408 (43:1165)****[4]**T. A. Burton,*Stability and periodic solutions of ordinary and functional differential equations*, Academic Press, Orlando, 1985. MR**837654 (87f:34001)****[5]**-,*Periodic solutions of nonlinear Volterra equations*, Funkcial. Ekvac.**27**(1985), 301-317. MR**794758 (87b:45004)****[6]**-,*Periodic solutions of functional differential equations*, J. London Math. Soc.**(2) (6) IV**(1985), 31-39.**[7]**J. K. Hale,*Theory of functional differential equations*, Springer-Verlag, New York, 1977. MR**0508721 (58:22904)****[8]**J. K. Hale and O. Lopes,*Fixed point theorems and dissipative processes*, J. Differential Equations**13**(1973), 391-402. MR**0333851 (48:12173)****[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**0267432 (42:2334)****[10]**T. Kaminogo,*Continuous dependence of solutions for integrodifferential equations with infinite delay*, preprint.**[11]**P. Massatt,*Stability and fixed points of point-dissipative systems*, J. Differential Equations**40**(1981), 217-231. MR**619135 (82j:47078)****[12]**R. Sine,*Remarks on a paper of Horn*, preprint.**[13]**D. R. Smart,*Fixed point theorems*, Cambridge Univ. Press, London and New York, 1980. MR**0467717 (57:7570)****[14]**S. Willard,*General topology*, Addison-Wesley, Reading, Mass., 1970. MR**0264581 (41:9173)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
47H10,
54H25

Retrieve articles in all journals with MSC: 47H10, 54H25

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0938677-9

Keywords:
Fixed points,
periodic solutions,
functional differential equations

Article copyright:
© Copyright 1988
American Mathematical Society