Have a personal or library account? Click to login
Existence and uniqueness of solutions for certain functional equations and system of functional equations arising in dynamic programming Cover

Existence and uniqueness of solutions for certain functional equations and system of functional equations arising in dynamic programming

By: Deepmala and  Ravi P. Agarwal  
Open Access
|Sep 2017

References

  1. [1] R. Bellman, Dynamic Programming, Princeton Univ. Press, Princeton, 1957.
  2. [2] R. Bellman and E. S. Lee, Functional equations arising in dynamic pro- gramming, Aequationes Math. 17, 1-18 (1978).10.1007/BF01818535
  3. [3] P. C. Bhakta and S. Mitra, Some existence theorems for functional equations arising in dynamic programming, J. Math. Anal. Appl. 98, 348-362 (1984).10.1016/0022-247X(84)90254-3
  4. [4] P. C. Bhakta and S. R. Choudhury, Some existence theorems for functional equations arising in dynamic programming II, J. Math. Anal. Appl. 131, 217-231 (1988).10.1016/0022-247X(88)90201-6
  5. [5] D. W. Boyd and J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20, 458-464 (1969).10.1090/S0002-9939-1969-0239559-9
  6. [6] S. S. Chang, Some existence theorems of common and coincidence solutions for a class of functional equations arising in dynamic programming, Appl. Math. Mech., 12, 33-39 (1991).10.1007/BF02018064
  7. [7] 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, 468-479 (1991).10.1016/0022-247X(91)90319-U
  8. [8] G. Jiang, S. M. Kang and Y. C. Kwun, Solvability and algorithms for functional equations originating from dynamic programming, Fixed Point Theory and Applications, Volume 2011, Article ID 701519, 30 pages, doi: 10.1155/2011/701519.
  9. [9] Z. Liu, Existence theorems of solutions for certain classes of functional equations arising in dynamic programming, J. Math. Anal. Appl., 262, 529-553 (2001).10.1006/jmaa.2001.7551
  10. [10] Z. Liu and S. M. Kang, Existence and uniqueness of solutions for two classes of functional equations arising in dynamic programming, Acta Mathematicae Applicatae Sinica. English Series, Vol. 23, No. 2, 195-208 (2007).10.1007/s10255-007-0363-6
  11. [11] Z. Liu and J. S. Ume, On properties of solutions for a class of functional equations arising in dynamic programming, Journal of Optimization Theory and Applications, 117, no. 3, 533-551 (2003).10.1023/A:1023945621360
  12. [12] Z. Liu, R. P. Agarwal and S. M. Kang, On solvability of functional equations and system of functional equations arising in dynamic programming, J. Math. Anal. Appl. 297, 111-130 (2004).10.1016/j.jmaa.2004.04.049
  13. [13] Z. Liu, S. M. Kang and J. S. Ume, Solvability and convergence of iterative algorithms for certain functional equations arising in dynamic programming, Optimization, 59, 887-916 (2010).10.1080/02331930902884182
  14. [14] Z. Liu, J. S. Ume and S. M. Kang, Some existence theorems for functional equations arising in dynamic programming, J. Korean Math. Soc. 43, 11 - 28 (2006).10.4134/JKMS.2006.43.1.011
  15. [15] Z. Liu, J. S. Ume and S. M. Kang, Some existence theorems for functional equations and system of functional equations arising in dynamic programming, Taiwanese Journal of Mathematics, 14, 1517-1536 (2010).10.11650/twjm/1500405965
  16. [16] Z. Liu, Y. Xu, J. S. Ume and S .M. Kang, Solutions to two functional equations arising in dynamic programming, J. Comput. Appl. Math. 192, 251-269 (2006).10.1016/j.cam.2005.04.033
  17. [17] H. K. Pathak and Deepmala, Existence and uniqueness of solutions of functional equations arising in dynamic programming, Appl. Math. Comp., 218 (2012) 7221-7230.10.1016/j.amc.2011.12.093
  18. [18] W. B. Powell, Dynamic Programming: Solving the Curses of Dimensionality, John Wiley and Sons, Inc., Hoboken, New Jersey, 2007.10.1002/9780470182963
DOI: https://doi.org/10.1515/auom-2016-0006 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 3 - 28
Submitted on: Jul 1, 2015
Accepted on: Sep 1, 2015
Published on: Sep 21, 2017
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2017 Deepmala, Ravi P. Agarwal, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.