Common Fixed Point Theorems in Bipolar Metric Spaces with Applications to Integral Equations

  • Authors

    • B. Srinuvasa Rao
    • G. N.V.Kishore
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.26662
  • Bipolar metric space, common fixed point, completeness, coincidence point, Covariant and contravariant maps, weakly compatible.

  • This paper establishes the existence of coincidence fixed-point and common fixed-point results for two mappings in a complete bipolar metric spaces. Some interesting consequences of our results is achieved. Finally, an illustration which presents the applicability of the results is achieved.

     

     

  • References

    1. [1] Ali Mutlu, Kübra Özkan, Utku Gürdal (2017), Coupled fixed point theorems on bipolar metric spaces. European journal of pure and applied mathematics. Vol. 10, No. 4, 655-667.

      [2] Ali Mutlu, Utku Gürdal (2016), Bipolar metric spaces and some fixed point theorems. J. Nonlinear Sci. Appl. 9(9), 5362-5373.

      [3] Ansari AH, Ege O, Radenovi´c, S (2017) , Some fixed point results on complex valued Gb- metric spaces. RACSAM, Doi: 10.1007/s13398-017-0391-x.

      [4] Banach S (1922), Sur les operations dans les ensembles abstraits etleur applications aux equations integrals. Fund. Math.3. 133-181.

      [5] Berinde, V (2009), A common fixed point theorem for compatible quasi contractive self- mappings in metric spaces. Appl. Math. Comput. 213(2), 348-354.

      [6] Chandok S, Choudhury B. S, Metiya N (2015), Some fixed point results in ordered metric spaces for rational type expressions with auxiliary functions. J. Egypt. Math. Soc. 23(1), 95-101. doi: 10. 1016/j. joems. 2014.02.002.

      [7] Dosenovi´c, T, Radenovi´c, S (2017), some critical remarks on the paper "An essential remark on fixed point results on multiplicative metric spaces". Adv. Math. Stud. 10(1), 20-24.

      [8] Dutta P.N, Choudhury B.S (2008), A generalization of contraction principle in metric spaces. Fix. Point Theo. Appl, 18,
      Article ID:406368.

      [9] Geraghty M (1973), on contractive mappings. Proc. Am. Math.
      Soc.40, 604-608.

      [10] Jankovi´c S, Golubovi´c Z, Radenovi´c S (2010), Compatible and weakly compatible mappings in cone metric spaces. Math. Comput. Model. 52, 1728-1738.

      [11] Jungck G (1966), Commuting mappings and common fixed points. Amer. Math. Monthly 73, 735-738.

      [12] Jungck G (1986), Compatible mappings and common fixed points. Int. J. Math. Math. Sci. 9, 771-779.

      [13] Mustafa Z, Huang H, Radenovi´c S (2016), Some remarks on the paper" Some fixed point generalizations are not real generalizations". J. Adv. Math. Stud. 9(1), 110-116.

  • Downloads

  • How to Cite

    Srinuvasa Rao, B., & N.V.Kishore, G. (2018). Common Fixed Point Theorems in Bipolar Metric Spaces with Applications to Integral Equations. International Journal of Engineering & Technology, 7(4.10), 1022-1026. https://doi.org/10.14419/ijet.v7i4.10.26662