충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제35권4호
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  • Pages.297-305
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  • 2022
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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HOMOTOPY RESULTS FOR THE BETTER ADMISSIBLE CHANDRABHAN TYPE MULTIMAPS

  • Kim, Hoonjoo (Department of Mathematics Education Sehan University)
  • 투고 : 2022.09.03
  • 심사 : 2022.11.25
  • 발행 : 2022.11.30
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초록

First, we generalize homotopy results of O'Regan [6] for Mönch type multimaps to Chandrabhan type multimaps. Second, we show that the better admissible Chandrabhan type multimaps have fixed point properties whenever their ranges are Klee approximable. Finally, we give examples of essential maps for various class of multimaps including 𝚽-condensing multimaps.

키워드

과제정보

Supported by the Sehan University Research Fund in 2022.

참고문헌

  1. R. P. Agarwal and D. O'Regan, Continuation theorems for countably condensing maps, Nonlinear Funct. Anal. Appl., 6 (2001), 1-18.
  2. R. P. Agarwal and D. O'Regan, Fixed point theory for set valued mappings between topological vector spaces having sufficiently many linear functionals, Comput. Math. Appl., 41 (2001), 917-928. https://doi.org/10.1016/S0898-1221(00)00329-1
  3. B. C. Dhage, On Monch type multi-valued maps and fixed points, Appl. Math. Lett., 20 (2007), 622-628. https://doi.org/10.1016/j.aml.2006.06.013
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  5. D. O'Regan, Coincidence theory for CS maps with applications, Commun. Pure Appl. Anal., 3 (1999), 433-446. https://doi.org/10.3934/cpaa.2004.3.433
  6. D. O'Regan, Homotopy results for admissible multifunctions, Nonlinear Funct. Anal. Appl., 6 (2001), 217-228.
  7. S. Park, Generalized Leray-Schauder principles for condensing admissible multifunctions, Ann. di Mat. Pura ed Appl., 172 (1997), 65-85. https://doi.org/10.1007/BF01782607
  8. 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
  9. S. Park, A unified fixed point theory of multimaps on topological vector spaces, J. Korean Math. Soc., 35 (1998), no. 4, 803-829. Corrections, ibid. 36 (1999), no. 4, 829-832.
  10. S. Park, Fixed points of multimaps in the better admissible class, J. Nonlinear Convex Anal., 5 (2004), 369-377.