DOI QR코드

DOI QR Code

FIXED POINT AND PERIODIC POINT THEOREMS ON METRIC SPACES

  • 투고 : 2011.09.26
  • 심사 : 2013.01.11
  • 발행 : 2013.02.15

초록

The aim of this paper is to establish a new fixed point theorem for a set-valued mapping defined on a metric space satisfying a weak contractive type condition and to establish a new common fixed point theorem for a pair of set-valued mappings defined on a metric space satisfying a weak contractive type inequality. And we give periodic point theorems for single-valued mappings defined on a metric space satisfying weak contractive type conditions.

키워드

참고문헌

  1. Ya. I. Alber, S. Guerre-Delabriere, Principles of weakly contractive maps in Hilbert spaces, in: New Results in Operator Theory, in: I. Goldberg, Yu. Lyu-bich (Eds.), Advances and Appl., vol. 98, Birkhauser Verlag, 1997, pp.7-22.
  2. M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341 (2008), 416-420. https://doi.org/10.1016/j.jmaa.2007.09.070
  3. M. Abbas, B. E. Rhoades, Fixed and periodic point results in cone metric spaces, Applied Mathematics Letters, (2008).
  4. R. P. Agarwal, M. A. El-Gebeily, D. O'Regan,Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008), 1-8. https://doi.org/10.1080/00036810701714164
  5. S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrales, Fund. Math. 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181
  6. S. H. Cho, J. S. Bae, Common fixed point theorems for mappings satisfying property (E:A) on cone metric spaces, Mathematical and Computer Modelling 53 (2011), 945-951. https://doi.org/10.1016/j.mcm.2010.11.002
  7. B. S. Choudhury, N. Metiya, Fixed points of weak contractions in cone metric spaces, Nonlinear Analysis 72 (2010), 1589-1593. https://doi.org/10.1016/j.na.2009.08.040
  8. B. S. Choudhury, P. Konar, B.E. Rhoades, N. Metiya, Fixed point theorems for generalized weakly contractive mappings, Nonlinear Analysis 74 (2011), 2116-2126. https://doi.org/10.1016/j.na.2010.11.017
  9. L. B. Ciric, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc. 45 (1974), 267-273.
  10. C. E. Chidume, H. Zegeye, S.J. Aneke, Approximation of fixed points of weakly contractive nonself maps in Banach spaces, J. Math. Anal. Appl. 270(1) (2002), 189-199. https://doi.org/10.1016/S0022-247X(02)00063-X
  11. D. Doric, Common fixed point for generalized $({\psi},{\varphi})$-weak contractions, Appl. Math. Lett. 22 (2009), 1896-1900. https://doi.org/10.1016/j.aml.2009.08.001
  12. P. N. Dutta, B. S. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory Appl. 2008 (2008) Article ID 406368. https://doi.org/10.1155/2008/406368
  13. J. X. Fang, Y. Gao, Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Anal. 70 (2009), 184-193. https://doi.org/10.1016/j.na.2007.11.045
  14. L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of con-tractive mappings, J. Math. Anal. Appl. 332(2) (2007), 1468-1476. https://doi.org/10.1016/j.jmaa.2005.03.087
  15. D. Ilic, V. Rakocevic, Quasi-contraction on cone metric spaces, Applied Mathematics Letters (2008).
  16. G. S. Jeong, B. E. Rhoades, Maps for which $F(T)=F(T^n)$, Fixed Point Theory Appl. 6 (2006), 72-105.
  17. M. A. Khamsi, V. Y. Kreinovich, Fixed point theorems for dissipative mappings in complete probabilistic metric spaces, Math. Jap. 44 (1996), 513-520.
  18. M. S. Khan, M. Swaleh, S. Sessa, Fixed points theorems by altering distances between the points, Bull. Aust. Math. Soc. 30 (1984), 1-9. https://doi.org/10.1017/S0004972700001659
  19. D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl. 334(1) (2007), 132-139. https://doi.org/10.1016/j.jmaa.2006.12.012
  20. V. Lakshmikantham, R.N. Mohapatra, Theory of Fuzzy Differential Equations and Inclusions, Taylor and Francis, London, 2003.
  21. Sh. Rezapour, R. Hamlbarani, Some notes on the paper "Cone metric spaces and fixed point theorems of contractive mappings", J. Math. Anal. Appl. 345 (2008), 719-724. https://doi.org/10.1016/j.jmaa.2008.04.049
  22. B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Analysis TMA 47(4)(2001), 2683-2693. https://doi.org/10.1016/S0362-546X(01)00388-1
  23. S. K. Yang, J. S. Bae, S. H. Cho, Coincidence and common fixed and periodic point theorems in cone metric spaces, Computers and Mathematics with Applications 61 (2011), 170-177. https://doi.org/10.1016/j.camwa.2010.10.031
  24. Q. Zhang, Y. Song, Fixed point theory for generalized A-weak contractions, Appl. Math. Lett. 22(1) (2009), 75-78. https://doi.org/10.1016/j.aml.2008.02.007