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
    https://doi.org/10.14419/ijet.v7i3.31.18277

    Received date: August 25, 2018

    Accepted date: August 25, 2018

    Published date: August 24, 2018

  • Bounded below function, Caristi’s mapping, C∗-algebra-valued Fuzzy soft metric, completeness, fixed point, Lower semi continuity.
  • Abstract

    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. Maji, Pk., Biswas, R and Roy, A. R., “Fuzzy soft Sets". Journal of
    2. Fuzzy Mathematics, Vol9, no3 (2001) 589-602.
    3. Thangaraj Beaula and Christinal Gunaseeli., on fuzzy soft
    4. metric spaces. Malaya J. Mat.2 (3) (2015), 438-442.
    5. Molodstov. D. A; “Fuzzy soft Sets"- First Result, Computers
    6. and Mathematics with Application, Vol.37 (1999) 19-31.
    7. Roy, S. and Samanta T. K., “A note on Fuzzy soft Topological
    8. Spaces", Annals of Fuzzy Mathematics and Informatics .2011.
    9. Tanay, B, and Kandemir, M. B.,”Topological Structure of fuzzy
    10. soft sets", Comput. Math. Appl. 61(2011), 2952-2957.
    11. Thangaraj Beaula, R.Raja., Completeness in Fuzzy Soft Metric
    12. Space. Malaya J. Mat. S (2) (2014), 197-20220(1), (2015), 55-67.
    13. 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.
    14. S. Banach, “Sur les operations dans les ensembles abstraits et leur application aux equations integrales”, Fund. Math, 3 , 1922, 133-181.1.
    15. Agarwal, RP, Khamsi, MA; Extension of Caristis´ fixed point
    16. theorem to vector valued metric space. Nonlinear Anal. TMA
    17. , 141-145(2011), doi: 10. 1016/j.na. 2010.08.025.
    18. Dur-e-Shehwar,et.al., Caristis´ fixed point theorem on C∗-algebra valued metric spaces. J. Nonlinear Sci. Appl.9 (2016), 584-588.
    19. Ekeland, I., On the variational principal. J. Math. Anal. Appl.
    20. (2), 324-353 (1974).
    21. Erdal Karapinar., Generalization of Caristi Kirks´ Theorem on partial metric spaces. Fixed point theory and Applications 2011, 2011:4.
    22. Farshid Khojasteh, et. al., some applications of Caristis´ fixed
    23. point theorem in metric spaces. Fixed point theory and Applications (2016), 2016:16.
    24. M. A. Khamsi, W. A. Kirk, An Introduction to metric spaces
    25. and fixed point theory, Wiley-Inter science, New York, (2001), http://dx.doi.org/10.1002/9781118033074.
    26. M. A. Khamsi., Remarks on Caristis´ fixed point theorem. Nonlinear Anal, 71 (2009), 227-231. 1.
    27. Wei-Shih Du., A Direct Proof of Caristis Fixed Point Theorem.
    28. Applied Mathematical Sciences, Vol. 10, 2016, no. 46, 2289 -
    29. Ma, ZH, Jiang, LN, Sun, HK. C∗ -algebra valued metric space
    30. and related fixed point theorems. Fixed point theory Appl.2014.
    31. ID 206(2014), 11 pages. 1, 2, 2.5, 3.6.
    32. G.J. Murphy., C∗ -algebras and Operator Theory. Academic press, Boston (1990).2.
  • Downloads

  • 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 and Technology, 7(3.31), 111-114. https://doi.org/10.14419/ijet.v7i3.31.18277