Kyungpook Mathematical Journal

  • 제55권1호
  • /
  • Pages.205-218
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  • 2015
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Some Common Fixed Point Theorems via Generalized c-Distance

  • 투고 : 2013.01.17
  • 심사 : 2014.06.20
  • 발행 : 2015.03.23
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초록

In this paper, we introduce the concept of generalized c-distance on a cone metric space and prove some common fixed point and coincidence point results by using this notion. Our results generalize and extend several well known comparable results in the literature.

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참고문헌

  1. T. Abdeljawad and E. Karapinar, Quasicone metric spaces and generalizations of Caristi Kirk's theorem, Fixed Point Theory and Applications, 2009(2009), Article ID 574387, 9 pages.
  2. M. Abbas and 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. H. Aydi, E. Karapinar and S. Moradi, Coincidence points for expansive mappings under c-distance in cone metric spaces, International Journal of Mathematics and Mathematical Sciences, 2012(2012), Article ID 308921, 11 pages.
  4. I. Beg and M. Abbas, Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition, Fixed Point Theory and Applications, 2006(2006), Article ID 74503, 7 pages.
  5. A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57(2000), 31-37.
  6. Z. M. Fadail and A. G. B. Ahmad, Common coupled fixed point theorems of single-valued mapping for c-distance in cone metric spaces, Abstract and Applied Analysis, 2012(2012), Article ID 901792, 24 pages.
  7. Z. M. Fadail, A. G. B. Ahmad and Z. Golubovic, Fixed point theorems of single-valued mapping for c-distance in cone metric spaces, Abstract and Applied Analysis, 2012(2012), Article ID 826815, 11 pages.
  8. L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332(2007), 1468-1476. https://doi.org/10.1016/j.jmaa.2005.03.087
  9. D. Ilic, V. Rakocevic, Common fixed points for maps on cone metric space, J. Math. Anal. Appl., 341(2008), 876-882. https://doi.org/10.1016/j.jmaa.2007.10.065
  10. G. Jungck, Common fixed points for noncontinuous nonself maps on non-metric spaces,Far East J. Math. Sci., 4(1996), 199-215.
  11. Osamu Kada, Tomonari Suzuki and Wataru Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japonica, 44(1996), 381-391.
  12. A. Kaewkhao, W. Sintunavarat, P. Kumam, Common Fixed Point Theorems of C-distance on Cone Metric Spaces, Journal of Nonlinear Analysis and Application, 2012(2012), Article ID jnaa-00137, 11 pages.
  13. S. K. Mohanta, A fixed point theorem via generalized w-distance, Bulletin of Mathematical Analysis and Applications, 3(2011), 134-139.
  14. S. K. Mohanta, Common fixed point theorems via w-distance, Bulletin of Mathematical Analysis and Applications, 3(2011), 182-189.
  15. S. K. Mohanta and Rima Maitra, Some fixed point theorems via w-distance on cone metric spaces, Global Journal of Science Frontier Research Mathematics and Decision Sciences, 12(2012), 42-52.
  16. J. O. Olaleru, Some generalizations of fixed point theorems in cone metric spaces, Fixed Point Theory and Applications, 2009(2009), Article ID 657914, 10 pages.
  17. B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Analysis: Theory, Methods and Applications, 47(2001), 2683-2693. https://doi.org/10.1016/S0362-546X(01)00388-1
  18. S. 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
  19. S. Rezapour, M. Derafshpour and R. Hamlbarani, A review on topological properties of cone metric spaces, in Proceedings of the Conference on Analysis, Topology and Applications (ATA'08), Vrnjacka Banja, Serbia, May-June 2008.
  20. P. Vetro, Common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo, 56(2007), 464-468. https://doi.org/10.1007/BF03032097
  21. S. Wang, B. Guo, Distance in cone metric spaces and common fixed point theorems, Applied Mathematics Letters, 24(2011), 1735-1739. https://doi.org/10.1016/j.aml.2011.04.031