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RECENT RESULTS AND CONJECTURES IN ANALYTICAL FIXED POINT THEORY

박세희
영남수학회 (Youngnam Mathematical Society)|2008.01|East Asian Mathematical Journal|제24권 제1호|pp. 11-20

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참고문헌

키워드

The Schauder conjectureweakly admissible setKlee approximableKakutani mapFan-Browder mapapproximable mapbetter admissible class of multimaps
주제분류수학

초록

We survey recent results and some conjectures in analytical fixed point theory. We list the known fixed point theorems for Kakutani maps, Fan-Browder maps, locally selectionable maps, approximable maps, admissible maps, and the better admissible class B of maps. We also give 16 conjectures related to that theory.

Abstract

We survey recent results and some conjectures in analytical fixed point theory. We list the known fixed point theorems for Kakutani maps, Fan-Browder maps, locally selectionable maps, approximable maps, admissible maps, and the better admissible class B of maps. We also give 16 conjectures related to that theory.

참고문헌 (27)

  1. I. D. Arandelovi´c, "On the weak admissibility on topological vector spaces and its applications in fixed point theory", Proc. II Mathematical Conf. in Priˇstina, pp.89~94 (1996)
  2. H. Ben-El-Mechaiekh, "Approachability and fixed points for non-convex set-valued maps", J. Math. Anal. Appl, 170, pp.477~500 (1992)
  3. H. Ben-El-Mechaiekh, "A Leray-Schauder type theorem for approximable maps", Proc. Amer. Math. Soc, 122, pp.105~109 (1994)
  4. F. E. Browder, "The fixed point theory of multi-valued mappings in topological vector spaces", Math. Ann, 177, pp.283~301 (1968)
  5. O. Hadˇzi´c, "Fixed Point Theory in Topological Vector Spaces", Univ˙ of Novi Sad, Novi Sad,, 337~ (1984)
  6. A. Idzik, "Almost fixed point theorems", Proc. Amer. Math. Soc, 104, pp.779~784 (1988)
  7. N. J. Kalton, "An F-space Sampler, Chap. 9", pp.198~219 (1985)
  8. N. T. Nhu, "The fixed point property for weakly admissble compact convex sets: Searching for a solution to Schauder’s conjecture", Topology Appl, 68, pp.1~12 (1996)
  9. T. Okon, "When graph meets diagonal: an approximative access to fixed point theory", 박사, pp.2001
  10. S. Park, "Some coincidence theorems on acyclic multifunctions and applications to KKM theory, Fixed Point Theory and Applications", pp.248~277 (1992), World Sci. Publ.
  11. S. Park, "Fixed point theory of multifunctions in topological vector spaces", J. Korean Math. Soc, 29, pp.191~208 (1992)
  12. S. Park, "Fixed point theory of multifunctions in topological vector spaces, II", J. Korean Math. Soc, 30, pp.413~431 (1993)
  13. S. Park, "Fixed points of approximable maps", Proc. Amer. Math. Soc, 124, pp.3109~3114 (1996)
  14. S. Park, "A unified fixed point theory of multimaps on topological vector spaces", J. Korean Math. Soc, 35, pp.803~829 (1998)
  15. S. Park, "Ninety years of the Brouwer fixed point theorem", Vietnam J. Math, 27, pp.193~232 (1999)
  16. S. Park, "Continuous selection theorems in generalized convex spaces", Numer. Funct. Anal. Optimiz, 20, pp.567~583 (1999)
  17. S. Park, "New topological versions of the Fan-Browder fixed point theorem", Nonlinear Anal, 47, pp.595~606 (2001)
  18. S. Park, "Fixed points, Roberts spaces, and the compact AR problem, Nonlinear Analysis and Convex Analysis (NACA2003, Tokyo, Japan)", pp.461~468 (2004), Yokohama Publ.
  19. S. Park, "The compact AR problem and related topics, Fixed Point Theory and Applications (Valencia, Spain, 2003)", pp.199~206 (2004), Yokohama Publ.
  20. S. Park, "On some conjectures and problems in analytical fixed point theory, revisited", RIMS Kokyuroku Kyoto University, 1365, pp.166~175 (2004)
  21. S. Park, "Multimaps having openness and the Birkhoff-Kellogg theorems", Indian J. Math, 46, pp.223~232 (2004)
  22. S. Park, "Recent results in analytical fixed point theory", Nonlinear Anal, 63, pp.977~986 (2005)
  23. S. Park, "Fixed points of multimaps in the better admissible class", J. Nonlinear Convex Anal, 5, pp.369~377 (2004)
  24. S. Park, "Fixed points of approximable or Kakutani maps in generalized convex spaces", J. Nonlinear Convex Anal, 7, pp.1~17 (2006)
  25. S. Park, "Fixed point theorems for better admissible multimaps on almost convex sets", J. Math. Anal. Appl, 329, pp.690~702 (2007)
  26. S. Park, "Remarks on Himmelberg-Idzik’s fixed point theorem", Acta Math. Viet, 25, pp.285~289 (2000)
  27. J. W. Roberts, "A compact convex set without extreme points", Studia Math, 60, pp.255~266 (1977)

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