The Existence of Fixed Points for Generalized Weak Contractions

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XUE, ZHIQUN

  • 투고 : 2014.12.04
  • 심사 : 2015.11.03
  • 발행 : 2015.12.23

초록

In this paper, we study the existence and uniqueness of fixed points for generalized weak contractions under some proper assumptions. Our theorems include the known results of [1]-[6].

키워드

Complete metric space;weak contraction;fixed point

참고문헌

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  4. P. N. Dutta and Binayak S. Choudhury, A Generalisation of Contraction Principle in Metric Spaces, Fixed Point Theory Appl., (2008), ID 406368, 8 pages doi:10.1155/2008/406368. https://doi.org/10.1155/2008/406368
  5. Q. N. Zhang and Y. S. Song, fixed point theory for generalized $\varphi$-weak contractions, Appl. Math. Lett., 22(1)(2009), 75-78. https://doi.org/10.1016/j.aml.2008.02.007
  6. D. Doric, Common fixed point for generalized (${\psi},{\varphi}$)-weak contractions, Appl. Math. Lett., 22(12)(2009), 1896-1900. https://doi.org/10.1016/j.aml.2009.08.001
  7. A. D. Arvanitakis, A proof of the generalized Banach contraction conjecture, Proc. Amer. Math. Soc., 131(12)(2003), 3647-3656. https://doi.org/10.1090/S0002-9939-03-06937-5
  8. S. V. R. Naidu, Some fixed point theorems in metric spaces by altering distances, Czech. Math. J., 53(1)(2003), 205-212. https://doi.org/10.1023/A:1022991929004
  9. K. P. R. Sastry and G. V. R. Babu, Some fixed point theorems by altering distances between the points, Indian J. Pure Appl. Math., 30(6)(1999), 641-647.
  10. K. P. R. Sastry, S. V. R. Naidu, G. V. R. Babu and G. A. Naidu, Generalization of common fixed point theorems for weakly commuting map by altering distances, Tamkang J. Math., 31(3)(2000), 243-250.

과제정보

연구 과제 주관 기관 : Natural Science Foundation of Hebei Province