Common fixed point theorem for a family of non-self mappings in cone metric spaces

Common fixed point theorem for a family of non-self mappings in cone metric spaces

In this paper, we prove a common xed point theorem for a family of non-self mappings in cone metric spaces (over a cone which is not necessarily normal). Our result generalizes and extends some recent results of Radenovic and Rhoades

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  • [1] Abbas. M. and Jungck, G. Common fixed point ivsidts for noncommuting mapping» without continuity in cone metric spaces, J. Math. Anal. Appl. 341, 416-420, 2008.
  • [2] Abbas, M. and Rhoades, B.E. Fixed and periodic point results m cone metric spaces, Appl. Math. Lett. 22, 511-515, 2009.
  • [3] Arshad, M., Azam. A. and Vetro, P. Some common fixed point results in cone uniform spaces, Fixed Point Theory and Appl., Article ID 493965, 11 Pages. doi.10.1155/2009/493965, 2009.
  • [4| Assad, N. A. and Kirk, W. A. Fixed paint theorems for set valued mappings of contractive type. Pacific J. Math. 43(3), 553-562, 1972.
  • [5] Azara, A. and Arshad, M. Common fixed points of generalized contractive maps in cone uniform sjfaces, Bull. Iranian Math. Soc. 35(2), 255-264, 2009,
  • [6] Di Bari, C. and Vetro, P. ip-pairs and common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo 57, 279-285, 2008.
  • [7] Di Bari, C. and Vetro, P. Weakly f-pairs and common fixed pointe in cone metric spaces, Rend. Circ. Mat. Palermo 58 , 125- 132, 2009.
  • [8] Hadzic. O. and Gajic, Lj. Coincidence points for set-valued mappings in convex metric spaces, Univ. U. Novom. Sadu. Zb. Rad. Prirod. Mat. Fak. Ser. Mat. 16(1), 13 25, 1986.
  • [9] Haghi, R. H. nd Rezapour, Sh. Fixed points of multifunction^ on regular cone metric spaces. Expo. Math. 28, 71-77, 2009.
  • [10] Haghi, R. H., Rezapour, Sh. and Shahzad, N. Some fixed point generalizations are not real generalizations. Nonlinear Anal. 74, 1799-1803, 2011.
  • [11] Huang. L. G. and Zhang, X. Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332, 1468-1476, 2007.
  • [12] Huang, X.J., Zhu, C. X. and Wen, X. Common fixed point theorem for four non-self mappings in cone metric spaces. Fixed Point Theory Appl., Article ID 983802, 14 pages, doi: 10.1155/2010/983802, 2010.
  • [13] Ilic, D. and Rakocevic, V. Common fixed points for maps on cone metric spacje. J. Math. Anal. Appl. 341 (2), 876-882, 2008.
  • [14] lmdad, M. and Khan, L. Some common fixed point theorems for a family of mappings in metrically convex spaces, Nonlinear Anal. 67, 2717-2726, 2007.
  • [15] Itndad, M. and Kumar, S. Flhoades-t.ype fixed point theorems for a pair of non-self mappings, Computer and Math, with Appl. 46, 919-927, 2003.
  • [16] Jankovic, S., Kadelburg, Z., Radenovic, S. and Rhoades, B.E. Assad-Kirk-tyj)e fixed point theorems for a pair of nonself mappings on _____;one metric spaces, Fixed Point Theory and Appl., 16 pages, Article ID 761086, doi: 10.1155/2009/761086, 2009.
  • [17] Jungck, G., Radenovic, S., Radojevic. S. and Rakocevic, V. Common fixed point theorems for Wfxikly compatible pairs on cone metric spaces, Fixed Point Theory and Appl., Article ID 643840, 13 pages, doi: 10.1155/2009/643840, 2009.
  • [18] Kadelburg,Z., Radenovic, S. and Rakocevic, V. Remarks on "quasi-contraction on a cone metric space", Appl. Math. Lett. 22, 1674-1679, 2009.
  • [19] Kadelburg, Z., Radenovic, S. and Rosic, B. Strict cont.mct.ive conditions and common fixed point theorems in cone metric spaces, Fixed Point Theory and Appl. 2009. Article ID 173838, 14 Pages, doi:10.1155/2009/173838, 2009,
  • [20] Klim, D. and Wardowski, D. Dynamic processes and fixed points of set-valued nonlinear contractions in cone metric spaces, Nonlinear Anal. 71, 5170-5175, 2009.
  • [21] Radenovic, S. Common fixed points under contractive conditions in cone metric spaces, Computer and Math, with Appl. 58. 1273-1278, 2009.
  • [22] Radenovic,S. and Rhoades, B. E. Fixed point theorem for two non-self mappings in cone metric spaces, Computer and Math, with Appl. 57, 1701-1707, 2009.
  • [23] Reich, S. Some remarks concerning contraction mappings, Canad. Math. Bull. 14. 121-124, 1971.
  • [24] Rezapour, Sh. and Haghi, R. H. Two results about fixed point, of multifunctions, Bull. Iranian Math. Soc. 36(2), 279 287, 2010.
  • [25] Rezapour, Sh. and Haghi, R. H. Fixed point of mxdtifunctions on cone metric spaces, Numer. Funct. Anal, and Opt. 30 (7-8), 825-832, 2009.
  • [26] Rezapour, Sh., Khandani, H. and Vaezpour, S. M. Efficacy of cones on topologuxd vector spaces and application to common fixed points of mxdtifunctions. Rend. Circ. Mat. Palermo 59. 185-197. 2010.
  • [27] Rezapour, Sh., Haghi, R. H. and Shahzad, N. Some Notes on fixed points of quasicontmction maps, Appl. Math. Lett. 23. 498-502. 2010.
  • [28] Rezapour, S. and Hamlbarani, R. Some notes on the paper "Cone metric spaces and fixed point theorems of contiuctive mappings", J. Math. Anal. Appl. 345, 719-724, 2008.
  • [29] Rhoades, B.E. A comparison of contractive definitions, Trans. Amer. Math. Soc. 226. 257 290. 1977.
  • [30] Vetro, P. Common fixed points in cone metric spaces> Rendiconti del circolo matematico d i Palermo, Serie II, Tomo LVI, 464 468, 2007.
  • [31] Wardowski, D. Endpoints and fixed points of set-valued contractions in cone metric space. Nonlinear Anal. 71, 512 516, 2009.
  • [32] Wong, Y.C. and Ng, K.F. Partially Ordered Topological Vector Spaces (Clarendon Press, Oxford, 1973).
  • [33] Zhu, C. X. and Chen, C. F. Calculations of mridorn fixed point, index, J. Math. Anal. Appl. 339, 839-844, 2008.
  • [34] Zhu, C. X. and Xu. Z. B. Random ambiguous point of random k(u)-set-contractive operator, .1. Math. Anal. Appl. 328. 2-6. 2007.