Fixed Point Theorems Under Caristi’s Type Map on C∗ -Algebra Valued Fuzzy Soft Metric Space

  • Authors

    • B Srinuvasa Rao
    • G N.V.Kishore
    • Trkd Vara Prasad
    2018-08-24
    https://doi.org/10.14419/ijet.v7i3.31.18277
  • Bounded below function, Caristi’s mapping, C∗-algebra-valued Fuzzy soft metric, completeness, fixed point, Lower semi continuity.
  • In this paper, we present the extension of Caristi’s fixed point theorems for mappings defined on C∗-algebra-valued Fuzzy soft metric spaces. We establish the existence of simple proof of caristi’s type fixed point theorems in C∗-algebra-valued Fuzzy soft metric spaces and we give some examples which supports our main results.

     

     

  • References

    1. [1] Maji, Pk., Biswas, R and Roy, A. R., “Fuzzy soft Sets". Journal of
      Fuzzy Mathematics, Vol9, no3 (2001) 589-602.

      [2] Thangaraj Beaula and Christinal Gunaseeli., on fuzzy soft
      metric spaces. Malaya J. Mat.2 (3) (2015), 438-442.

      [3] Molodstov. D. A; “Fuzzy soft Sets"- First Result, Computers
      and Mathematics with Application, Vol.37 (1999) 19-31.

      [4] Roy, S. and Samanta T. K., “A note on Fuzzy soft Topological
      Spaces", Annals of Fuzzy Mathematics and Informatics .2011.

      [5] Tanay, B, and Kandemir, M. B.,â€Topological Structure of fuzzy
      soft sets", Comput. Math. Appl. 61(2011), 2952-2957.

      [6] Thangaraj Beaula, R.Raja., Completeness in Fuzzy Soft Metric
      Space. Malaya J. Mat. S (2) (2014), 197-20220(1), (2015), 55-67.

      [7] Caristi, J., Fixed point theorems for mappings satisfying inwardness conditions. Trans. Amer. Math. Soc., 215 (1976), 241-251. http://dx.doi.org/10.1090/s0002-9947-1976-0394329-4.

      [8] S. Banach, “Sur les operations dans les ensembles abstraits et leur application aux equations integralesâ€, Fund. Math, 3 , 1922, 133-181.1.

      [9] Agarwal, RP, Khamsi, MA; Extension of Caristis´ fixed point
      theorem to vector valued metric space. Nonlinear Anal. TMA
      74, 141-145(2011), doi: 10. 1016/j.na. 2010.08.025.

      [10] Dur-e-Shehwar,et.al., Caristis´ fixed point theorem on C∗-algebra valued metric spaces. J. Nonlinear Sci. Appl.9 (2016), 584-588.

      [11] Ekeland, I., On the variational principal. J. Math. Anal. Appl.
      47(2), 324-353 (1974).

      [12] Erdal Karapinar., Generalization of Caristi Kirks´ Theorem on partial metric spaces. Fixed point theory and Applications 2011, 2011:4.

      [13] Farshid Khojasteh, et. al., some applications of Caristis´ fixed
      point theorem in metric spaces. Fixed point theory and Applications (2016), 2016:16.

      [14] M. A. Khamsi, W. A. Kirk, An Introduction to metric spaces
      and fixed point theory
      , Wiley-Inter science, New York, (2001), http://dx.doi.org/10.1002/9781118033074.

      [15] M. A. Khamsi., Remarks on Caristis´ fixed point theorem. Nonlinear Anal, 71 (2009), 227-231. 1.

      [16] Wei-Shih Du., A Direct Proof of Caristis Fixed Point Theorem.
      Applied Mathematical Sciences, Vol. 10, 2016, no. 46, 2289 -
      2294.

      [17] Ma, ZH, Jiang, LN, Sun, HK. C∗ -algebra valued metric space
      and related fixed point theorems. Fixed point theory Appl.2014.
      ID 206(2014), 11 pages. 1, 2, 2.5, 3.6.

      [18] G.J. Murphy., C∗ -algebras and Operator Theory. Academic press, Boston (1990).2.

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  • How to Cite

    Srinuvasa Rao, B., N.V.Kishore, G., & Vara Prasad, T. (2018). Fixed Point Theorems Under Caristi’s Type Map on C∗ -Algebra Valued Fuzzy Soft Metric Space. International Journal of Engineering & Technology, 7(3.31), 111-114. https://doi.org/10.14419/ijet.v7i3.31.18277