Research Article
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On Generalized (Ψ,φ)-Almost Weakly Contractive Maps in Generalized Fuzzy Metric Spaces

Year 2018, Issue: 25, 59 - 64, 06.10.2018

Maduraiveeran Jeyaraman Rengasamy Muthuraj Mangaiyarkarasu Sornavalli

Abstract

In
this paper, we come out with the approach of generalized  (Ψ,φ)-almost
weakly contractive maps in the context of generalized fuzzy metric spaces. We
prove theorem to show the existence of a fixed point and also provide an
example in support to our result.

Keywords

(Ψ φ)-almost weakly contractive map Fuzzy metric space Generalized fuzzy metric spaces

References

  • [1] Atanassov, K., Intuitionistic fuzzy sets, Fuzzy, Sets and Systems 20 (1986) 87–96.
  • [2] George, A. and Veeramani, P., On some results in fuzzy metric spaces, Fuzzy sets and Systems, (1994). 395–399.
  • [3] Kramosil, I. and Michalek, J., Fuzzy metric and statistical metric space, Kybernetika, 11(1975), 326-334.
  • [4] Sun, G. and Yang, K., Generalized fuzzy metric spaces with properties, Research Journal of Applied Sciences Eng. and Technology, Vol.2, (7), (2010), 673-678.
  • [5] Babu, G. V. R., Dasari Ratna babu, Kanuri Nageswara Rao, Bendi Venkata Siva Kumar, Fixed points of (Ψ,φ)-almost weakly contractive maps in G- metric Spaces, Applied Mathematical E-Notes 14 (2014), 69- 85.
  • [6] Berinde, V., Approximating fixed points of weak contractions using the picard Iteration, Nonlinear Anal. Forum, 9 (2004), 43- 53.
  • [7] Doric, D., Common fixed point for generalized (Ψ,φ) - weakly contractions, Appl. Math. Letter., 22 (2009), 1896-1900.
  • [8] Dutta, P. N. and Choudhury B. S., A generalization of contraction principle in metric spaces, Fixed point Theory and Appl., (2008), Article ID 406368.
  • [9] Harjani, J. and Sadarangani, K., Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Analy., 71 (2009) 3403-3410.
  • [10] Manthena P., Rangamma, M., Fixed points of of (Ψ,φ)-lmost weakly contractive maps in Fuzzy metric spaces, Advanced Fixed point theory, 6 (2016), No.4, 387-396.
  • [11] Rhoades, B. E., some theorems on weak contractive maps, Nonlinear Anal. 47(2001), 2683- 2693.
  • [12] Saha, P., A weak contraction in G- Complete Fuzzy metric space, Intern. J. Fuzzy Mathematical Archive 3 (2013), 100- 103.
  • [13] Schweizer, B. and Sklar, A., Statistical metric spaces, Pacific Journal of Math., 10 (1960), 313.
  • [14] Zang, Q. and Song, Y., Fixed point theory for generalized φ–weak contractions, Appl. Math. Letter, 22 (2009), 75-78.
  • [15] Zadeh, L. A, Fuzzy sets, Infor. and Control., (1965), 8338 – 353.

Year 2018, Issue: 25, 59 - 64, 06.10.2018

Maduraiveeran Jeyaraman Rengasamy Muthuraj Mangaiyarkarasu Sornavalli

Abstract

References

  • [1] Atanassov, K., Intuitionistic fuzzy sets, Fuzzy, Sets and Systems 20 (1986) 87–96.
  • [2] George, A. and Veeramani, P., On some results in fuzzy metric spaces, Fuzzy sets and Systems, (1994). 395–399.
  • [3] Kramosil, I. and Michalek, J., Fuzzy metric and statistical metric space, Kybernetika, 11(1975), 326-334.
  • [4] Sun, G. and Yang, K., Generalized fuzzy metric spaces with properties, Research Journal of Applied Sciences Eng. and Technology, Vol.2, (7), (2010), 673-678.
  • [5] Babu, G. V. R., Dasari Ratna babu, Kanuri Nageswara Rao, Bendi Venkata Siva Kumar, Fixed points of (Ψ,φ)-almost weakly contractive maps in G- metric Spaces, Applied Mathematical E-Notes 14 (2014), 69- 85.
  • [6] Berinde, V., Approximating fixed points of weak contractions using the picard Iteration, Nonlinear Anal. Forum, 9 (2004), 43- 53.
  • [7] Doric, D., Common fixed point for generalized (Ψ,φ) - weakly contractions, Appl. Math. Letter., 22 (2009), 1896-1900.
  • [8] Dutta, P. N. and Choudhury B. S., A generalization of contraction principle in metric spaces, Fixed point Theory and Appl., (2008), Article ID 406368.
  • [9] Harjani, J. and Sadarangani, K., Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Analy., 71 (2009) 3403-3410.
  • [10] Manthena P., Rangamma, M., Fixed points of of (Ψ,φ)-lmost weakly contractive maps in Fuzzy metric spaces, Advanced Fixed point theory, 6 (2016), No.4, 387-396.
  • [11] Rhoades, B. E., some theorems on weak contractive maps, Nonlinear Anal. 47(2001), 2683- 2693.
  • [12] Saha, P., A weak contraction in G- Complete Fuzzy metric space, Intern. J. Fuzzy Mathematical Archive 3 (2013), 100- 103.
  • [13] Schweizer, B. and Sklar, A., Statistical metric spaces, Pacific Journal of Math., 10 (1960), 313.
  • [14] Zang, Q. and Song, Y., Fixed point theory for generalized φ–weak contractions, Appl. Math. Letter, 22 (2009), 75-78.
  • [15] Zadeh, L. A, Fuzzy sets, Infor. and Control., (1965), 8338 – 353.
There are 15 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Maduraiveeran Jeyaraman

Rengasamy Muthuraj

Mangaiyarkarasu Sornavalli

Publication Date October 6, 2018
Submission Date May 22, 2018
Published in Issue Year 2018 Issue: 25

Cite

APA Jeyaraman, M., Muthuraj, R., & Sornavalli, M. (2018). On Generalized (Ψ,φ)-Almost Weakly Contractive Maps in Generalized Fuzzy Metric Spaces. Journal of New Theory(25), 59-64.
AMA Jeyaraman M, Muthuraj R, Sornavalli M. On Generalized (Ψ,φ)-Almost Weakly Contractive Maps in Generalized Fuzzy Metric Spaces. JNT. October 2018;(25):59-64.
Chicago Jeyaraman, Maduraiveeran, Rengasamy Muthuraj, and Mangaiyarkarasu Sornavalli. “On Generalized (Ψ,φ)-Almost Weakly Contractive Maps in Generalized Fuzzy Metric Spaces”. Journal of New Theory, no. 25 (October 2018): 59-64.
EndNote Jeyaraman M, Muthuraj R, Sornavalli M (October 1, 2018) On Generalized (Ψ,φ)-Almost Weakly Contractive Maps in Generalized Fuzzy Metric Spaces. Journal of New Theory 25 59–64.
IEEE M. Jeyaraman, R. Muthuraj, and M. Sornavalli, “On Generalized (Ψ,φ)-Almost Weakly Contractive Maps in Generalized Fuzzy Metric Spaces”, JNT, no. 25, pp. 59–64, October 2018.
ISNAD Jeyaraman, Maduraiveeran et al. “On Generalized (Ψ,φ)-Almost Weakly Contractive Maps in Generalized Fuzzy Metric Spaces”. Journal of New Theory 25 (October 2018), 59-64.
JAMA Jeyaraman M, Muthuraj R, Sornavalli M. On Generalized (Ψ,φ)-Almost Weakly Contractive Maps in Generalized Fuzzy Metric Spaces. JNT. 2018;:59–64.
MLA Jeyaraman, Maduraiveeran et al. “On Generalized (Ψ,φ)-Almost Weakly Contractive Maps in Generalized Fuzzy Metric Spaces”. Journal of New Theory, no. 25, 2018, pp. 59-64.
Vancouver Jeyaraman M, Muthuraj R, Sornavalli M. On Generalized (Ψ,φ)-Almost Weakly Contractive Maps in Generalized Fuzzy Metric Spaces. JNT. 2018(25):59-64.
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