Two fixed point theorems in generalized metric spaces

  • Authors

    • Salwa S Abed Baghdad university, College of Education for pure sciences, department of mathematics
    • Hadeel H. Luaibi Baghdad university, College of Education for pure sciences, department of mathematics
    2016-02-12
    https://doi.org/10.14419/ijasp.v4i1.5715
  • G-Metric Spaces, Fixed Points, Coupled Fixed Points, Implicit Conditions.

  • In this paper, we prove there exists a coupled fixed point for a set- valued contraction mapping defined on X× X , where X is incomplete ordered G-metric. Also, we prove the existence of a unique fixed point for single valued mapping with respect to implicit condition defined on a complete G- metric.

  • References

    1. [1] S.B. Nadler, Multi-valued Contraction Mappings, Pacific J Math. 30(1969), pp. 475–478. http://dx.doi.org/10.2140/pjm.1969.30.475.

      [2] L. Gorniewicz , Topological Fixed Point Theory of Multivalued Mappings, Kluwer Academic Publishers (1999) .

      [3] M.A. Al-Thagafi, N. Shahzad, Coincidence Point Generalized I- Nonexpansive Multi-maps and Applications, Nonlinear Anal. 67(2007), pp. 2180–2188. http://dx.doi.org/10.1016/j.na.2006.08.042.

      [4] Z. Mastafa and B. Sims, Fixed Point Theorems for Contractive Mappings in Complete G-Metric Spaces, Fixed point Theory and Applications, Vol. (2009), pp.10

      [5] Z. Mustafa, (2005),'' A New Structure for Generalized Metric Spaces with Applications to Fixed Point Theory'', University of Newcastle, Newcastle, UK.

      [6] Z. Mustafa, W. Shatanawi , M. Bataineh, Existence of Fixed Point Results in G-Metric Spaces , Int J Math Math Sci. (2009) , pp. 10. http://dx.doi.org/10.1155/2009/283028.

      [7] BE. Rhoades, M. Abbas, Common Fixed Point Results for Non-Commuting Mappings without Continuity in Generalized Metric Spaces, Appl. Math. Comput. 215(2009), pp.262–269. http://dx.doi.org/10.1016/j.amc.2009.04.085.

      [8] R. Saadati, SM. Vaezpour, P. Vetro, BE. Rhoades Fixed Point Theorems in Generalized Partially Ordered G-Metric Spaces, Math Comput. Model. 52(2010), pp. 797–801. http://dx.doi.org/10.1016/j.mcm.2010.05.009.

      [9] A.C.M. Ran, M.C.B. Reurings, A Fixed Point Theorem in Partially Ordered Sets and Some Applacations to Matrix Equations, Proc. Amer. Math. Soc. 123(2004), pp.1435-1443. http://dx.doi.org/10.1090/S0002-9939-03-07220-4.

      [10] T.G. Bhaskar, V. Lakshmikantham, Fixed Point Theorems in Partially Ordered Metric Spaces and Applications, Nonlinear Anal. 65(2006), pp. 1379–1393. http://dx.doi.org/10.1016/j.na.2005.10.017.

      [11] V. Lakshmikantham, L. Ćirić, Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces, Nonlinear Anal. 70(2009), pp.4341–4349. http://dx.doi.org/10.1016/j.na.2008.09.020.

      [12] S.K. Mohanta and S. Mohanta, A Common Fixed Point Theorem in G-Metric Spaces, CUBO A Mathematical Journal, Vol.14, (October 2012) No 03, pp.85–101.

      [13] N. Tahat, H. Aydi, E. Karapinar and W. Shatanawi, Common Fixed Points For Single-valued and Multi-valued Maps Satisfying A Generalized Contraction in G-Metric Spaces, Tahat et al. Fixed Point Theory and Applications,(2012) pp.48

      [14] M. Abbasa, A. R. Khanb, T.Nazira, Common Fixed Point Of Multivalued Mappings In Ordered Generalized Metric Spaces, Filomat 26:5 ( 2012), pp.1045–1053. http://dx.doi.org/10.2298/FIL1205045A.

  • Downloads