Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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GENERALIZED FIXED POINT THEOREMS IN CONE METRIC SPACES

  • Received : 2012.08.12
  • Accepted : 2012.09.16
  • Published : 2012.09.30
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Abstract

In this paper we introduce the property (C), which is a cone metric extension of the usual metric property (E,A) and consider fixed point theorems for generalized contractive mappings under suitable conditions in cone metric spaces without normal cones.

Keywords

References

  1. L.G. Huang and X. Zhang, Cone metric spaces and xed point theorems of con- tractive mappings, J. Math. Anal. Appl. 332 (2007), 1468-1476. https://doi.org/10.1016/j.jmaa.2005.03.087
  2. D. Wardowski, On set-valued contractions of Nadler type in cone metric spaces, Appl. Math. Lett. 24 (2011), 275-278. https://doi.org/10.1016/j.aml.2010.10.003
  3. I. Altun, B. Damjanovic and D. Djoric, Fixed point and common xed point theorems on ordered cone metric spaces, Appl. Math. Lett. 23 (2010), 310-316. https://doi.org/10.1016/j.aml.2009.09.016
  4. D. Ilic and V. Rakocevic, Quasi-contraction on a cone metric space, Appl. Math. Lett. 22 (2009), 728-731. https://doi.org/10.1016/j.aml.2008.08.011
  5. D. Klim and D. Wardowski, Dynamic processes and xed points of set-valued nonlinear contraction in cone metric spaces, Nonlinear Anal. 71 (2009), 5170- 5175. https://doi.org/10.1016/j.na.2009.04.001
  6. B.C. Choudhury and N. Metiya, Fixed points of weak contractions in cone metric spaces, Nonlinear Anal. 72 (2010), 1589-1593. https://doi.org/10.1016/j.na.2009.08.040
  7. P.N. Dutta and B.S. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory Appl. 2008 (2008), Article ID 406386, 8pages.
  8. M. Aamri and D.E. Moutawakil, Some new common xed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002), 181-188. https://doi.org/10.1016/S0022-247X(02)00059-8
  9. R.P. Pant, Fixed points of nonexpansive mappings and a generalized notion of compactness, Bull. Calcutta Math. Soc. 99 (1) (2007), 45-52.
  10. M. Abbas and G. Jungck, Common xed point results for noncommuting map- pings without continuity in cone metric spaces, J. Math. Anal. Appl. 341 (2008), 416-420. https://doi.org/10.1016/j.jmaa.2007.09.070
  11. H.R. Zhao, B.S. Lee and N.J. Huang, Common xed points for generalized weakly contractive mappings in cone metric spaces, Nonlinear Anal. Forum 16 (2011), 77-84.

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  1. FIXED POINTS AND COMMON FIXED POINTS THEOREMS IN CONE METRC-LIKE SPACES vol.37, pp.1, 2021, https://doi.org/10.7858/eamj.2021.010