대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제45권3호
  • /
  • Pages.573-585
  • /
  • 2008
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

COMMON FIXED POINT THEOREMS FOR CONTRACTIVE TYPE MAPPINGS AND THEIR APPLICATIONS IN DYNAMIC PROGRAMMING

  • Liu, Zeqing (DEPARTMENT OF MATHEMATICS LIAONING NORMAL UNIVERSITY) ;
  • Wang, Lili (DEPARTMENT OF MATHEMATICS LIAONING NORMAL UNIVERSITY) ;
  • Kim, Hyeong-Kug (DEPARTMENT OF MATHEMATICS GYEONGSANG NATIONAL UNIVERSITY) ;
  • Kang, Shin-Min (DEPARTMENT OF MATHEMATICS AND THE RESEARCH INSTITUTE OF NATURAL SCIENCE GYEONGSANG NATIONAL UNIVERSITY)
  • 발행 : 2008.08.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

A few sufficient conditions for the existence and uniqueness of fixed point and common fixed point for certain contractive type mappings in complete metric spaces are provided. Several existence and uniqueness results of solution and common solution for some functional equations and system of functional equations in dynamic programming are discussed by using the fixed point and common fixed point theorems presented in this paper.

키워드

참고문헌

  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, New Jersey, 1957
  3. R. Bellman and E. S. Lee, Functional equations in dynamic programming, Aequationes Math. 17 (1978), no. 1, 1-18 https://doi.org/10.1007/BF01818535
  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, A note on unique common fixed point, Bull. Calcutta Math. Soc. 85 (1993), no. 5, 469-472
  8. 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
  9. Z. Liu, Coincidence theorems for expansion mappings with applications to the solutions of functional equations arising in dynamic programming, Acta Sci. Math. (Szeged) 65 (1999), no. 1-2, 359-369
  10. Z. Liu, Compatible mappings and fixed points, Acta Sci. Math. (Szeged) 65 (1999), no. 1-2, 371-383
  11. 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 (2004), no. 1, 111-130 https://doi.org/10.1016/j.jmaa.2004.04.049
  12. Z. Liu and J. S. Ume, On properties of solutions for a class of functional equations arising in dynamic programming, J. Optim. Theory Appl. 117 (2003), no. 3, 533-551 https://doi.org/10.1023/A:1023945621360
  13. H. K. Pathak and B. Fisher, Common fixed point theorems with applications in dynamic programming, Glas. Mat. Ser. III 31(51) (1996), no. 2, 321-328
  14. B. N. Ray, On common fixed points in metric spaces, Indian J. Pure Appl. Math. 19 (1988), no. 10, 960-962
  15. S. S. Zhang, Some existence theorems of common and coincidence solutions for a class of systems of functional equations arising in dynamic programming, Appl. Math. Mech. 12 (1991), no. 1, 31-37

피인용 문헌

  1. Fixed point theorems for mappings satisfying contractive conditions of integral type and applications vol.2011, pp.1, 2011, https://doi.org/10.1186/1687-1812-2011-64
  2. On the solvability of a functional equation vol.60, pp.3, 2011, https://doi.org/10.1080/02331930903121311
  3. A new type of contractive multivalued operators vol.137, pp.1, 2013, https://doi.org/10.1016/j.bulsci.2012.07.001
  4. Fixed points of Suzuki type generalized multivalued mappings in fuzzy metric spaces with applications vol.2015, pp.1, 2015, https://doi.org/10.1186/s13663-015-0284-7
  5. Some Suzuki-type fixed point theorems for generalized multivalued mappings and applications vol.2011, pp.1, 2011, https://doi.org/10.1186/1687-1812-2011-40
  6. Metric-Like Space and Suzuki Type Common Fixed Point Results with (W.C.C) Conditions pp.1793-7183, 2020, https://doi.org/10.1142/S1793557120500667
  7. Common Fixed-Point Theorems for Hybrid Generalized (F, 𝜑)-Contractions Under the Common Limit Range Property with Applications vol.69, pp.11, 2018, https://doi.org/10.1007/s11253-018-1470-7