Some New CARISTI Type Results in Metric Spaces with an Application to Graph Theory

  • Authors

    • G. Adilakshmi
    • G. N.V.Kishore
    • W. Sridhar
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.20917
  • Metric spaces, W - compatible maps, fixed point, Caristi type mapping.

  • Abstract

    In this paper we proved some new Caristi type common fixed point theorems for four maps in a metric space and we gave an applications to Graph theory.

     

     

  • References

    1. [1] Abbas M, Alikhan M, S.Radenovi´ c, “Common coupled ï¬xed point theorems in cone metric spaces for w-compatible mappingsâ€, Applied Mathematics and Computation., 217(1) (2010), 195 - 202.

      [2] Aydi H, “Some coupled ï¬xed point results on partial metric spacesâ€, International Journal of Mathematics and Mathematical Sciences., 2011, Article ID 647091.

      [3] Caristi J, “Fixed point theorems for mappings satisfying inwardness conditionsâ€,Transactions of the American Mathematical Society., 215 (1976), pp. 241-251.

      [4] Ekeland I, “On the variational principleâ€, Journal of Mathematical Analysis and Applications., 47(2) (1974), 324-353.

      [5] Karap nar E, “Generalizations of Caristi Kirk’s Theorem on Partial metric Spacesâ€, Fixed Point Theory and. Appl., 2011, 2011:4.

      [6] Lakshmikantham V, ´Ciri´c Lj, “Coupled ï¬xed point theorems for nonlinear contractions in partially ordered metric spacesâ€, Nonlinear Analysis., 70 (2009), 4341 - 4349.

      [7] Alfuraidan MR and Khamsi MA, “Caristi ï¬xed point theorem in Metric space with a Graphâ€, Hindawi Publishing corporation Abstract and Applied Analysis., 2014, Article ID 303484.

      [8] P. C. Bhakta, T. Basu, “Some ï¬xed point theorems on metric spacesâ€, J. Indian Math. Soc., 45 (1981),399-404.

      [9] Rao KPR, Kishore GNV, Nguyen Van Luong, “A unique common coupled ï¬xed point theorem for four maps under ψ - φ contractive condition in partial metric spacesâ€, CUBO A Mathematical Journal.,14(3) (2012), 115 - 127.

      [10] Rao KPR, Kishore GNV, Raju VCC, “A coupled ï¬xed point theorem for two pairs of w - compatible maps using altering distance function in partial metric spaceâ€, Journal of Advanced Research in Pure Mathematics., 4(4) (2012), 96 - 114.

      [11] Banach S, “Sur les operations dans les ensembles abstraits et leur application aux equations integralsâ€, Fund. Math., 3(1) (1922), 133 181.

  • Downloads

  • How to Cite

    Adilakshmi, G., N.V.Kishore, G., & Sridhar, W. (2018). Some New CARISTI Type Results in Metric Spaces with an Application to Graph Theory. International Journal of Engineering & Technology, 7(4.10), 303-305. https://doi.org/10.14419/ijet.v7i4.10.20917

    Received date: 2018-10-04

    Accepted date: 2018-10-04

    Published date: 2018-10-02