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SOME EXISTENCE THEOREMS FOR FUNCTIONAL EQUATIONS ARISING IN DYNAMIC PROGRAMMING

  • LIU ZEQING (Department of Mathematics Liaoning Normal University) ;
  • UME JEONG SHEOK (Department of Applied Mathematics Changwon National University) ;
  • KANG SHIN MIN (Department of Mathematics and Research Institute of Natural Science Gyeongsang National University)
  • Published : 2006.01.01

Abstract

The existence, uniqueness and iterative approximation of solutions for a few classes of functional equations arising in dynamic programming of multistage decision processes are discussed. The results presented in this paper extend, improve and unify the results due to Bellman [2, 3], Bhakta-Choudhury [6], Bhakta-Mitra [7], and Liu [12].

References

  1. R. Baskaran and P. V. Subrahmanyam, A note on the solution of a class of functional equations, Appl. Anal. 22 (1986), no. 3-4, 235-241 https://doi.org/10.1080/00036818608839621
  2. R. Bellman, Dynamic programming, Princeton University Press, Princeton, N. J., 1957
  3. R. Bellman and M. Roosta, A technique for the reduction of dimensionality in dynamic programming, J. Math. Anal. Appl. 88 (1982), no. 2, 543-546 https://doi.org/10.1016/0022-247X(82)90212-8
  4. P. C. Bhakta and S. R. Choudhury, Some existence theorems for functional equations arising in dynamic programming II, J. Math. Anal. Appl. 131 (1988), no. 1, 217-231 https://doi.org/10.1016/0022-247X(88)90201-6
  5. P. C. Bhakta and S. Mitra, Some existence theorems for functional equations arising in dynamic programming, J. Math. Anal. Appl. 98 (1984), no. 2, 348-362 https://doi.org/10.1016/0022-247X(84)90254-3
  6. S. S. Chang and Y. H. Ma, Coupled fixed points for mixed monotone condensing operators and an existence theorem of the solutions for a class of functional equations arising in dynamic programming, J. Math. Anal. Appl. 160 (1991), no. 2, 468-479 https://doi.org/10.1016/0022-247X(91)90319-U
  7. Z. Liu, Coincidence theorems for expansive mappings with applications to the solutions of functional equations arising in dynamic programming, Acta Sci. Math. (Szeged) 65 (1999), no. 1-2, 359-369
  8. Z. Liu, Compatible mappings and fixed points, Acta Sci. Math. (Szeged) 65 (1999), no. 1-2, 371-383
  9. R. Bellman and E. S. Lee, Functional equations in dynamic programming, Ae-quationes Math. 17 (1978), no. 1, 1-18 https://doi.org/10.1007/BF01818535
  10. Z. Liu, Existence theorems of solutions for certain classes of functional equations arising in dynamic programming, J. Math. Anal. Appl. 262 (2001), no. 2, 529-553 https://doi.org/10.1006/jmaa.2001.7551
  11. R. Bellman, Methods of Non-linear analysis, Vol. II, Mathematics in Science and Engineering, Vol. 61-II, Academic Press, New York-London, 1973
  12. S. S. Chang, Some existence theorems of common and coincidence solutions for a class of functional equations arising in dynamic programming, Appl. Math. Mech.(English Ed.) 12 (1991), no. 1, 33-39 https://doi.org/10.1007/BF02018064

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