Common fixed point theorems for weakly compatible non-self mappings in metric spaces of hyperbolic type

  • Authors

    • Kanayo Eke Covenant University

    Received date: January 5, 2016

    Accepted date: January 28, 2016

    Published date: February 22, 2016

    https://doi.org/10.14419/gjma.v4i1.5733
  • Common Fixed Points, Generalized Contractive Mappings, Metric Space of Hyperbolic Type, Nonself Mappings, Weakly Compatible Mappings.

  • Abstract

    In this paper, we establish common fixed point theorems for a pair of weakly compatible nonself mappings  satisfying generalized contractive  conditions in metric space of hyperbolic type. The results generalize and extend some results in literature.

  • References

    1. [1] W. A. Kirk, Krasnoselskii’s iteration process in hyperbolic space, Numer. Funct. Anal. And Optimiz., 4(1982), 371-381.

      [2] N. A. Assad, On a fixed point theorem in Banach space, Tamkang J. Math. ,7(1976), 91-94.

      [3] N. A. Assad and W. A. Kirk, Fixed point theorems for set-valued mappings of contractive type, Pacific J. Math. , 43(1972), 553-562.

      [4] G. Jungck, S. Radenovic, V. Radejovic, V. Rakocevic, Common fixed point theorems for weakly compatible pairs on cone metric spaces, Fixed Point Theory Appl., 2009, Article ID 643840(2009), doi:10.1155/2009/643840.

      [5] R. Sumitra, V. R. Uthariaraj, R.Hemavathy, P. Vijayaraju, Common fixed point theorem for non-self mappings satisfying generalized Ciric type contraction condition in cone metric space, Fixed Point Theory and Applications, (2010), Article ID 408086, 17 pages.

      [6] S. Radenovic and B. E. Rhoades, Fixed point theorem for two non-self mappings in cone metric spaces, Computers and Mathematics with Applications, 57(2009), 1701-1707.

      [7] S. Jankovic, Z. Kadelburg, S. Radenovic, BE Rhoades, Assad-Kirk type fixed point theorems for a pair of non-self mappings on cone metric spaces, Fixed Point Theory Appl., 2009, Article ID 761086(2009), doi:10.1155/2009/761086.

      [8] L. B. Ciric, Contractive-type non-self mappings on metric spaces of hyperbolic type, J. Math. Anal. Appl., 317(2006), 28-42.

      [9] L. Ciric, V. Rakocevic, S. Radenovic, M. Rajovic, R. Lazovic, Common fixed point theorems for non-self mappings in metric spaces of hyperbolic type, Journal of Computational and Applied Mathematics, 233(2010), 2966-2974.

      [10] W. Takahashi, A convexity in metric spaces and nonexpansive mappings, I. Kodai Math. Sem. Rep. 22(1970), 142-149.

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  • How to Cite

    Eke, K. (2016). Common fixed point theorems for weakly compatible non-self mappings in metric spaces of hyperbolic type. Global Journal of Mathematical Analysis, 4(1), 2-5. https://doi.org/10.14419/gjma.v4i1.5733

    Received date: January 5, 2016

    Accepted date: January 28, 2016

    Published date: February 22, 2016