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The Existence of Fixed Points for Generalized Weak Contractions

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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].

Abstract

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].

참고문헌 (10)

  1. Ya. I. Alber., "Principles of weakly contractive maps in Hilbert spaces, In : I. Gohberg, Yu. Lyubich(Eds. ), New Results in Operator Theory", Advances and Appl., 98, pp.7~22 (1997)
  2. B. E. Rhoades, "Some theorems on weakly contractive maps", Nonlinear Anal, 47(4), pp.2683~2693 (2001)
  3. D. W. Boyd., "On nonlinear contractions", Proc. Amer. Math. Soc, 20(2), pp.458~464 (1969)
  4. P. N. Dutta., "A Generalisation of Contraction Prin- ciple in Metric Spaces", Fixed Point Theory Appl. (2008)[DOI]
  5. Q. N. Zhang., "xed point theory for generalized φ-weak contractions", Appl. Math. Lett, 22(1), pp.75~78 (2009)
  6. D. Doric, "Common xed point for generalized(ψ, φ)-weak contractions", Appl. Math. Lett, 22(12), pp.1896~1900 (2009)
  7. A. D. Arvanitakis, "A proof of the generalized Banach contraction conjecture", Proc. Amer. Math. Soc, 131(12), pp.3647~3656 (2003)
  8. S. V. R. Naidu, "Some xed point theorems in metric spaces by altering distances", Czech. Math. J, 53(1), pp.205~212 (2003)
  9. K. P. R. Sastry., "Some xed point theorems by altering distances between the points", Indian J. Pure Appl. Math, 30(6), pp.641~647 (1999)
  10. K. P. R. Sastry., "Generalization of common xed point theorems for weakly commuting map by altering distances", Tamkang J. Math, 31(3), pp.243~250 (2000)

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