DOI QR코드

DOI QR Code

COMMON FIXED POINT RESULTS FOR NON-COMPATIBLE R-WEAKLY COMMUTING MAPPINGS IN PROBABILISTIC SEMIMETRIC SPACES USING CONTROL FUNCTIONS

  • 투고 : 2018.10.03
  • 심사 : 2019.07.27
  • 발행 : 2019.09.30

초록

In common fixed point problems in metric spaces several versions of weak commutativity have been considered. Mappings which are not compatible have also been discussed in common fixed point problems. Here we consider common fixed point problems of non-compatible and R-weakly commuting mappings in probabilistic semimetric spaces with the help of a control function. This work is in line with research in probabilistic fixed point theory using control functions. Further we support our results by examples.

키워드

참고문헌

  1. C.T. Aage, B.S. Choudhury and K. Das, Some fixed point results in fuzzy metric spaces using a control function, Surveys in Mathematics and its Applications 12 (2017), 23-34.
  2. B.S. Choudhury and K. Das, A new contraction principle in Menger spaces, Acta Mathematica Sinica 24 (8) (2008), 1379-1386. https://doi.org/10.1007/s10114-007-6509-x
  3. B.S. Choudhury , P.N. Dutta and K. Das, A fixed points result in Menger space using a real function, Acta. Math. Hungar. 122 (2008), 203-216. https://doi.org/10.1007/s10474-008-7242-3
  4. B.S. Choudhury and K. Das, A coincidence point result in Menger spaces using a control function, Chaos, Solitons and Fractals 42 (2009), 3058-3063. https://doi.org/10.1016/j.chaos.2009.04.020
  5. B.S. Choudhury, K.P. Das and P. Das, Coupled coincidence point results for compatible mappings in partially ordered fuzzy metric spaces, Fuzzy Sets and Systems 222 (2013), 84-97. https://doi.org/10.1016/j.fss.2012.07.012
  6. B.S. Choudhury, K.P. Das and P. Bhattacharya, A Common Fixed Point Theorem for Weakly Compatible Mappings in Complete Fuzzy Metric Space, Review Bulletin of the Calcutta Mathematical Society 21 (2013), 181-192.
  7. B.S. Choudhury, K.P. Das and P. Das, Coupled coincidence point results in partially ordered fuzzy metric spaces, Annals of Fuzzy Mathematics and Informatics 7 (2014), 619-628.
  8. P.N. Dutta, B.S. Choudhury and K. Das, Some fixed point results in Menger spaces using a control function, Surveys in Mathematics and its Applications 4 (2009), 41-52.
  9. S.N. Jesic, N.A. Cirovic and, D. O'Regan, Altering distances and a common fixed point theorem in Menger probabilistic metric spaces, FILOMAT 31 (2017), 175-181. https://doi.org/10.2298/FIL1702175J
  10. C. Ji, C. Xhu, and Z. Wu, Some new fixed point theorems in generalized probabilistic metric space, J. Nonlinear Sci. Appl. 9 (2016), 3735-3743. https://doi.org/10.22436/jnsa.009.06.24
  11. G. Jungk, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986), 771-779. https://doi.org/10.1155/S0161171286000935
  12. O. Hadzic and E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, 2001.
  13. M.S. Khan, M. Swaleh and S. Sessa , Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc. 30 (1984), 1-9. https://doi.org/10.1017/S0004972700001659
  14. P. Ma, J. Guan, Y. Tang, Xu, and Y. Su, $\psi$-contraction and (${\phi}-{\psi}$)-contraction in Menger probabilistic metric space, Springer Plus 5 (2016), 1-12. https://doi.org/10.1186/s40064-015-1659-2
  15. K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. USA 28 (1942), 535-537. https://doi.org/10.1073/pnas.28.12.535
  16. D. Mihet, Altering distances in probabilistic Menger spaces, Nonlinear Analysis 71 (2009), 2734-2738. https://doi.org/10.1016/j.na.2009.01.107
  17. S.V.R. Naidu, Some fixed point theorems in metric spaces by altering distances, Czechoslovak Mathematical Journal 53 (2003), 205-212. https://doi.org/10.1023/A:1022991929004
  18. R.P. Pant, Common fixed points of weakly commuting mappings, Math. Student 62 (1993), 97-102.
  19. R.P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994), 436-440. https://doi.org/10.1006/jmaa.1994.1437
  20. R.P. Pant, Common fixed points of contractive maps, J. Math. Anal. Appl. 226 (1998), 251-258. https://doi.org/10.1006/jmaa.1998.6029
  21. R.P. Pant, R-weakly commutativity and common fixed points, Soochow J, Math. 25 (1999), 37-42.
  22. R.P. Pant, Common fixed points under strict contractive conditions, J. Math. Anal. Appl. 248 (2000), 327-332. https://doi.org/10.1006/jmaa.2000.6871
  23. V. Pant, Contractive conditions and common fixed points, Acta Math. Acad. Paed. Nyir. 24 (2008), 257-266.
  24. K.P.R. Sastry and G.V.R. Babu, Some fixed point theorems by altering distances between the points, Ind. J. Pure. Appl. Math. 30 (6) (1999), 641-647.
  25. K.P.R. Sastry, S.V.R. Naidu, G.V.R. Babu and G.A. Naidu, Generalisation of common fixed point theorems for weakly commuting maps by altering distances, Tamkang Journal of Mathematics 31 (3) (2000), 243-250. https://doi.org/10.5556/j.tkjm.31.2000.399
  26. B. Schweizer and A. Sklar, Probabilistic Metric Spaces, Elsevier, North-Holland, (1983).
  27. V.M. Sehgal and A.T. Bharucha-Reid, Fixed point of contraction mappings on PM space, Math. Sys. Theory 6 (2) (1972), 97-100. https://doi.org/10.1007/BF01706080
  28. S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. 32 (1982), 149-153.
  29. N. Wairojjana, T. Dosenovic, D. Rakik, and D. Gopal, P. Kumam, An altering distance function in fuzzy metric fixed point theorems, Fixed Point Theory and Applications 2015 (2015 : 69), 1-19. https://doi.org/10.1186/1687-1812-2015-1
  30. C. Zaharia and N. Cirovic, A probabilistic fixed point result using altering distance function, Journal of Function Spaces, Volume 2015, Article ID 919202, 6 pages, http://dx.doi.org/10.1155/2015/919202