Fixed point results of fuzzy $(\theta, \mathcal {L})-$ weak contraction in $\mathbb{G}$-metric space

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria

2 Department of Mathematics, COMSATS University,Chak Shahzad, Islamabad,44000, Pakistan

Abstract

In this paper, the notion of fuzzy $(\theta, \mathcal {L})$-weak contraction in $\mathbb{G}-$metric space is introduced, and sufficient conditions for the existence of fuzzy fixed points for such mappings are investigated. Relevant illustrative examples are constructed to support the assumptions of our established theorems. It is observed that the principal ideas obtained herein extend and subsume some well-known results in the corresponding literature. A few of these special cases of our results are noted and discussed as corollaries

Keywords

References

[1] I. Y. Alber and S. D. Guerre, Principle of weakly contractive maps in Hilbert spaces, In New Results Oper. Theory Appl., 8(1997) 7-22.
[2] M. A. Alghamdi and E. Karapinar, G 􀀀   􀀀  􀀀contractive type mappings in G-metric spaces, Fixed Point Theory Appl.,4 (2013) 123-129.
[3] M. Asadi, E. Karapnar and P. Salimi, A new approach to G-metric and related  fixed point theorems, J. Ineq. Appl.,6(2013) 454-463.
[4] A. Azam, Fuzzy  xed points of fuzzy mappings via a rational inequality, Hacett. J. Math. Stat., 40(2011) 421-431.
[5] V. Berinde, On the approximation of  xed points of weak contractive mappings, Carpathian J. Math., (2003) 7-22.
[6] M. Berinde and V. Berinde, On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl., 326(2007) 772-782.
[7] J. Chen, C. Zhu and L. Zhu, A note on some  xed point theorems on G-metric spaces, J. Appl. Anal. Comp., 11 (2021), 101-112.
[8] M. M. Frechet, Sur quelques points du calcul fonctionnel, Rendiconti del Circolo Matematico di Palermo, 22(1906), 1-72.
[9] S. Heilpern, Fuzzy mappings and  xed point theorem, J. Math. Anal. Appl., 83(1981) 566-569.
[10] N. Hussain, V. Parvaneh and F. Golkarmanesh, Coupled and tripled coincidence point results under (F; g)􀀀invariant sets in Gb􀀀metric spaces and G- 􀀀admissible mappings, Math. Sci., 9(2015), 11-26.
[11] A. J. Jiddah, M. Alansari, O. S. K. Mohamed, M. S. Shagari and A. A. Bakery, Fixed Point Results of Jaggi-Type Hybrid Contraction in Generalized Metric Space, J. Function Spaces, vol. 2022, Article ID 2205423, 9 pages, DOI: 10.1155/2022/2205423.
[12] A. J. Jiddah, M. Noorwali, M. S. Shagari, S. Rashid and F. Jarad, Fixed Point Results of a New Family of Hybrid Contractions in Generalized Metric Space with Applications, AIMS Mathematics, 7(2022) 17894-17912 , DOI: 10.3934/math.2022986.
[13] A. Kaewcharoen, A., and Kaewkhao, A., Common  xed points for single-valued and multi-valued mappings in G-metric spaces, Int. J. Math. Anal, 5(2011) 1775-1790.
[14] W. Lodwick, Fuzzy, Possibility, Probability, and Generalized Uncertainty Theory in Mathematical Analysis, J. Mahani Math. Res., 10(2021) 73-101 . doi:10.22103/jmmrc.2021.18055.1160
[15] S. S. Mohammed and A. Azam, Fixed points of soft-set valued and fuzzy set-valued maps with applications, J. Intel. Fuz. Sys., 37(2019) 3865-3877. https://doi.org/10.3233/jifs-190126.
[16] S. S. Mohammed and A. Azam, Integral type contractions of soft set-valued maps with application to neutral di erential equation, AIMS Mathematics, 5(2019) 342-358. https://doi.org/10.3934/math.2020023.
[17] S. S. Mohammed, K. Shazia, A. Hassen and U. G.Yae, Fuzzy  xed point results in convex C-algebra-valued metric spaces, J. Function Spaces, Volume 2022, Article ID 7075669, 7 pages https://doi.org/10.1155/2022/7075669
[18] S. S. Mohammed, On Bilateral fuzzy contractions, Anal., Approx. Comp., 12(2020) 1-13.
[19] S. K. Mohanta, Some  xed point theorems in G-metric spaces, Analele Universitatii" Ovidius" Constanta-Seria Matematica, 20(2012) 285-306 .
[20] Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonl. convex Anal., 7(2006) 289-297.
[21] Z. Mustafa and B. Sims, Fixed point theorems for contractive mappings in complete-metric spaces. Fixed point theory and Applications, 2009(2009) 91-99.
[22] Z. Mustafa, H. Obiedat and F. Awawdeh, Some  xed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl., vol. 2008, Article ID 189870, 12 Pages, DOI: 10.1155/2008/189870.
[23] Z. Mustafa, M. Arshad, S. U. Khan, J. Ahmad M. Jaradat, Common  xed points for multivalued mappings in G-metric spaces with applications, J. Nonlinear Sci. Appl, 10 (2017) 2550-2564.
[24] S. B. Nadler, Multi-valued contraction mappings, Pac. J. Math., 30(1969), 475-488.
[25] H. Poincare, Surless courbes de ne barles equations di erentiate less, J. de Math, 2(1886), 54-65.
[26] B. Samet, C. Vetro and P. Vetro, Fixed point theorems for   􀀀  􀀀contractive type mappings, Nonl. Anal.: Theory, Methods Appl., 75(2012) 2154-2165.
[27] M. Shamsizadeh, M. Zahedi, K. Abolpour, Kleen's Theorem for BL-general L-fuzzy automata, J. Mahani Math. Res., 10(2021) 125-144. doi: 10.22103/jmmrc.2021.17171.1134
[28] L. Zhu, C. X. Zhu and C. F. Chen, Common  xed point theorems for fuzzy mappings in G-metric spaces, Fixed Point Theory Appl., 2012(2012) 159-165.

Files

History

  • Receive Date: 07 August 2022
  • Revise Date: 25 September 2022
  • Accept Date: 11 November 2022

Share

How to cite

Statistics