Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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NOTE ON THE RESULTS WITH LOWER SEMI-CONTINUITY

  • Chen, Yuqing (Department of Mathematics, Fushan University) ;
  • Cho, Yeol-Je (Department of Mathematics Education, College of Education, Gyeongsang National University) ;
  • Yang, Li (Department of Mathematics, Mianyang Teacher′s College)
  • Published : 2002.11.01
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Abstract

In this paper, we introduce the concept of lower semi-continuous from above functions and show that many well-known results, such as Ekland's and Caristi's theorems, remain also true under lower semi-continuous from above functions.

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References

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  2. Optima and Equilibria J. P. Aubin
  3. Applied Nonlinear Analysis J. P. Aubin;I. Ekland
  4. Trans. Amer. Math. Soc. v.303 A smooth variational principle with applications to subdifferentiability and to differentiability of conver functions J. M. Borwein;D. Preiss https://doi.org/10.1090/S0002-9947-1987-0902782-7
  5. Trans. Amer. Math. Soc. v.215 Fixed point teorems for mappings satisfying inwardness conditions J. Caristi https://doi.org/10.2307/1999724
  6. J. Math. Anal. Appl. v.47 On the variational principle I. Ekland https://doi.org/10.1016/0022-247X(74)90025-0
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