- Volume 34 Issue 3
DOI QR Code
FIXED POINTS AND ALTERNATIVE PRINCIPLES
- Park, Se-Hie (The National Academy of Sciences, Department of Mathematical Sciences, Seoul National University) ;
- Kim, Hoon-Joo (Department of Mathematical Education, Sehan University)
- Received : 2012.08.06
- Accepted : 2012.08.26
- Published : 2012.09.25
In a recent paper, M. Balaj [B] established an alternative principle. The principle was applied to a matching theorem of Ky Fan type, an analytic alternative, a minimax inequality, and existence of solutions of a vector equilibrium theorem. Based on the first author's fixed point theorems, in the present paper, we obtain generalizations of the main result of Balaj [B] and their applications.
- M. Balaj, Alternative principles and their applications, J. Glob. Optim. DOI 10.1007/s10898-010-9612-y.
- K. Fan, Some properties of convex sets reated to fixed point theorem, Math. Ann. 266 (1984), 519-537. https://doi.org/10.1007/BF01458545
- M. Lassonde, Fixed points of Kakutani factorizable multifunctions, J. Math. Anal. Appl. 152 (1990), 46-60. https://doi.org/10.1016/0022-247X(90)90092-T
- E. Michael, Continuous selections. I, Ann. Math. 63(2) (1956), 361-381. https://doi.org/10.2307/1969615
- E. Michael, A theorem on semi-continuous set-valued functions, Duke Math. J. 26 (1959), 647-651. https://doi.org/10.1215/S0012-7094-59-02662-6
- S. Park, Fixed point theory of multifunctions in topological vector spaces, II, J. Korean Math. Soc. 30 (1993), 413-431.
- S. Park, Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps, J. Korean Math. Soc. 31 (1994), 493-520.
- S. Park, Coincidence theorems for the better admissible multimaps and their applications, Nonlinear Anal. 30 (1997), 4183-4191. https://doi.org/10.1016/S0362-546X(97)00385-4
- S. Park, A unified fixed point theory of multimaps on topological vector spaces, J. Korean Math. Soc. 35 (1998)
- J. Korean Math. Soc. 36 (1999), 829-832.
- S. Park, Fixed points of multimaps in the better admissible class, J. Nonlinear Convex Anal. 5 (2004), 369-377.
- S. Park, Fixed point theorems for better admissible multimaps on almost convex sets, J. Math. Anal. Appl. 329 (2007), 690-702. https://doi.org/10.1016/j.jmaa.2006.06.066
- S. Park, Applications of multimap classes in abstract convex spaces, J. Nat. Acad. Sci., ROK, Nat. Sci. Ser. 51(2) (2012), to appear.