Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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A COMMON FIXED POINT RESULT FOR A (${\psi}$, ${\varphi}$)-WEAK CONTRACTIVE CONDITION TYPE

  • Aydi, Hassen (Universite de Sousse. Institut Superieur d'Informatique et des Technologies de Communication de Hammam Sousse)
  • 투고 : 2011.03.08
  • 심사 : 2012.01.27
  • 발행 : 2012.09.30
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초록

We establish a coincidence and a common fixed point result for four mappings involving a (${\psi}$, ${\varphi}$)-weak contractive condition type on a complete metric space. We take on ${\psi}$ and ${\varphi}$ the same conditions given by Popescu [Fixed points for (${\psi}$, ${\varphi}$)-weak contractions, Appl. Math. Lett. 24 (2011), 1-4].

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참고문헌

  1. M. Abbas and D. Doric, Common fixed point theorem for four mappings satisfying generalized weak contractive condition, Filomat 24, (2) (2010), 1-10. https://doi.org/10.2298/FIL1002001A
  2. Ya.I. Alber and S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert spaces, in: I. Gohberg, Yu. Lyubich (Eds.), New Results in Theory Operator Theory, in: Advances and Appl. Birkhauser, Basel, vol. 98, 1997, pp. 7-22.
  3. H. Aydi, Coincidence and common fixed point results for contraction type maps in partially ordered metric spaces, International. J. Math. Anal. 5 (13) (2011), 631-642.
  4. H. Aydi, Some fixed point results in ordered partial metric spaces, J. Nonlinear Sciences. Appl. 4 (3) (2011), 210-217. https://doi.org/10.22436/jnsa.004.03.04
  5. H. Aydi, Fixed point results for weakly contractive mappings in ordered partial metric spaces, J. Advanced Math. Studies 4 (2) (2011), 1-12.
  6. H. Aydi, Fixed point theorems for generalized weakly contractive condition in ordered partial metric spaces, Journal of Nonlinear Analysis and Optimization: Theory and Applications, 2 (2) (2011), 33-48.
  7. H. Aydi, Common fixed point results for mappings satisfying (${\psi},{\phi}$)-weak contractions in ordered partial metric spaces, International J. Mathematics and Statistics, 12 (2) (2012), 53-64.
  8. H. Aydi, H.K. Nashine, B. Samet and H. Yazidi, Coincidence and common fiixed point results in partially ordered cone metric spaces and applications to integral equations, Nonlinear Anal. 74 (17) (2011), 6814-6825. https://doi.org/10.1016/j.na.2011.07.006
  9. H. Aydi, B. Damjanovic, B. Samet and W. Shatanawi: Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces, Math. Comput. Modelling 54 (2011), 2443-2450. https://doi.org/10.1016/j.mcm.2011.05.059
  10. H. Aydi, W. Shatanawi and C. Vetro: On generalized weakly G-contraction mapping in G-metric spaces, Comput. Math. Appl. 62 (2011), 4222-4229. https://doi.org/10.1016/j.camwa.2011.10.007
  11. H. Aydi, W. Shatanawi and M. Postolache: Coupled fixed point results for (${\psi},{\phi}$)-weakly contractive mappings in ordered G-metric spaces, Comput. Math. Appl. 63 (2012), 298-309. https://doi.org/10.1016/j.camwa.2011.11.022
  12. D.W. Boyd and T.S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458-464. https://doi.org/10.1090/S0002-9939-1969-0239559-9
  13. D. Doric, Common fixed point for generalized ${\psi},{\phi}$) weak contractions, Appl. Math. Lett. 22 (2009), 1896.1900. https://doi.org/10.1016/j.aml.2009.08.001
  14. P.N. Dutta and B.S. Choudhury, A generalization of contraction principle in metric spaces, Fixed Point Theory Appl. Volume (2008), Article ID 406368.
  15. G. Jungck and B.E. Rhoades, Fixed points for set valued functions without continiuty, Indian. J. Pur. Appl. Math. 29 (1998), 227-238.
  16. O. Popescu, Fixed points for (${\psi},{\phi}$)-weak contractions, Appl. Math. Lett. 24 (2011), 1-4. https://doi.org/10.1016/j.aml.2010.06.024
  17. S. Reich, Some fixed point problems, Atti Acad. Naz. Lincei Ren. Cl. Sci. Fis. Mat. Natur. 57 (1975), 194-198.
  18. B.H. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. 47 (2001), 2683-2693. https://doi.org/10.1016/S0362-546X(01)00388-1
  19. B.D. Rouhani and S. Moradi, Common fixed point of multivalued generalized ${\psi}$-weak contractive mappings, Fixed Point Theory Appl. Volume (2010), Article ID 708984.
  20. Q. Zhang and Y. Song, Fixed point theory for generalized ${\psi}$-weak contractions, Appl. Math. Lett. 22 (2009), 75-78. https://doi.org/10.1016/j.aml.2008.02.007

피인용 문헌

  1. On Fixed Points of $ \alpha \text{-}\psi $ -Contractive Multivalued Mappings in Cone Metric Spaces vol.2013, pp.None, 2012, https://doi.org/10.1155/2013/313782