## Fixed point theory for compact upper semi-continuous or lower semi-continuous set valued maps

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**125**(1997), 875-881 Request permission

## Abstract:

Fixed point theory is presented for compact u.s.c. and l.s.c. set valued maps.## References

- H. Ben–El–Mechaiekh, Fixed points for compact set–valued maps,
*Q. and A. in General Topology*,**10**(1992), 153–156. - H. Ben-El-Mechaiekh and P. Deguire,
*Approachability and fixed points for nonconvex set-valued maps*, J. Math. Anal. Appl.**170**(1992), no. 2, 477–500. MR**1188567**, DOI 10.1016/0022-247X(92)90032-9 - H. Ben-El-Mechaiekh and A. Idzik,
*A Leray-Schauder type theorem for approximable maps*, Proc. Amer. Math. Soc.**122**(1994), no. 1, 105–109. MR**1212281**, DOI 10.1090/S0002-9939-1994-1212281-2 - H. Ben–El–Mechaiekh and M.Oudadess, Some selection theorems without convexity,
*Jour. Math. Anal. Appl.*,**195**(1995), 614–618. - Romulus Cristescu,
*Topological vector spaces*, Editura Academiei, Bucharest; Noordhoff International Publishing, Leyden, 1977. Translated from the Romanian by Mihaela Suliciu. MR**0454552** - Josef Daneš,
*Generalized concentrative mappings and their fixed points*, Comment. Math. Univ. Carolinae**11**(1970), 115–136. MR**263063** - James Dugundji and Andrzej Granas,
*Fixed point theory. I*, Monografie Matematyczne [Mathematical Monographs], vol. 61, Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1982. MR**660439** - Massimo Furi and Patrizia Pera,
*A continuation method on locally convex spaces and applications to ordinary differential equations on noncompact intervals*, Ann. Polon. Math.**47**(1987), no. 3, 331–346. MR**927581**, DOI 10.4064/ap-47-3-331-346 - Andrzej Granas,
*On the Leray-Schauder alternative*, Topol. Methods Nonlinear Anal.**2**(1993), no. 2, 225–231. MR**1251936**, DOI 10.12775/TMNA.1993.040 - C. J. Himmelberg, J. R. Porter, and F. S. Van Vleck,
*Fixed point theorems for condensing multifunctions*, Proc. Amer. Math. Soc.**23**(1969), 635–641. MR**246175**, DOI 10.1090/S0002-9939-1969-0246175-1 - E. Michael,
*A selection theorem*, Proc. Amer. Math. Soc.**17**(1966), 1404–1406. MR**203702**, DOI 10.1090/S0002-9939-1966-0203702-5 - E. Michael and C. Pixley,
*A unified theorem on continuous selections*, Pacific J. Math.**87**(1980), no. 1, 187–188. MR**590875**, DOI 10.2140/pjm.1980.87.187 - D. O’Regan, Fixed point theory for the sum of two operators,
*Applied Mathematics Letters*,**9**(1996), 1–8. - D. O’Regan, Some fixed point theorems for concentrative mappings between locally convex linear topological spaces,
*Nonlinear Anal.*, to appear. - A. J. B. Potter,
*An elementary version of the Leray-Schauder theorem*, J. London Math. Soc. (2)**5**(1972), 414–416. MR**312342**, DOI 10.1112/jlms/s2-5.3.414 - C. H. Su and V. M. Sehgal,
*Some fixed point theorems for condensing multifunctions in locally convex spaces*, Proc. Amer. Math. Soc.**50**(1975), 150–154. MR**380530**, DOI 10.1090/S0002-9939-1975-0380530-7 - E. Tarafdar and R. Výborný,
*Fixed point theorems for condensing multivalued mappings on a locally convex topological space*, Bull. Austral. Math. Soc.**12**(1975), 161–170. MR**383167**, DOI 10.1017/S0004972700023789 - Eberhard Zeidler,
*Nonlinear functional analysis and its applications. I*, Springer-Verlag, New York, 1986. Fixed-point theorems; Translated from the German by Peter R. Wadsack. MR**816732**, DOI 10.1007/978-1-4612-4838-5

## Additional Information

**Donal O’Regan**- Affiliation: Department Of Mathematics, University College Galway, Galway, Ireland
- MR Author ID: 132880
- Email: Donal.ORegan@UCG.IE
- Received by editor(s): October 16, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**125**(1997), 875-881 - MSC (1991): Primary 47H10, 47H04
- DOI: https://doi.org/10.1090/S0002-9939-97-03746-5
- MathSciNet review: 1371137