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AIMS Mathematics

2022, Volume 7, Issue 5: 8558-8573. doi: 10.3934/math.2022477
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Certain new aspects in fuzzy fixed point theory

  • 1.
    ORIC, University of management and technology, Lahore, Pakistan
  • 2.
    Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
  • Received: 20 November 2021 Revised: 12 January 2022 Accepted: 17 January 2022 Published: 28 February 2022

  • MSC : 47H10, 54H25

  • We will establish several fixed point results in new introduced spaces in this manuscript known as fuzzy rectangular metric-like spaces and rectangular b-metric-like spaces. These new results and spaces will improve the approach of existing ones in the literature. Few non-trivial examples and an application also verify the uniqueness of solution.

    Citation: Umar Ishtiaq, Aftab Hussain, Hamed Al Sulami. Certain new aspects in fuzzy fixed point theory[J]. AIMS Mathematics, 2022, 7(5): 8558-8573. doi: 10.3934/math.2022477

    Related Papers:

  • We will establish several fixed point results in new introduced spaces in this manuscript known as fuzzy rectangular metric-like spaces and rectangular b-metric-like spaces. These new results and spaces will improve the approach of existing ones in the literature. Few non-trivial examples and an application also verify the uniqueness of solution.


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    [1] L. A. Zadeh, Fuzzy sets, In: Fuzzy sets, fuzzy logic, and fuzzy systems, 1996,394-432. https://doi.org/10.1142/9789814261302_0021
    [2] I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11 (1975), 336-344.
    [3] O. Kaleva, S. Seikkala, On fuzzy metric spaces, Fuzzy Sets Syst., 12 (1984), 215-229. https://doi.org/10.1016/0165-0114(84)90069-1 doi: 10.1016/0165-0114(84)90069-1
    [4] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst., 64 (1994), 395-399. https://doi.org/10.1016/0165-0114(94)90162-7 doi: 10.1016/0165-0114(94)90162-7
    [5] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets Syst., 27 (1988), 385-389. https://doi.org/10.1016/0165-0114(88)90064-4 doi: 10.1016/0165-0114(88)90064-4
    [6] K. Javed, F. Uddin, H. Aydi, M. Arshad, U. Ishtiaq, H. Alsamir, On fuzzy b-metric-like spaces, J. Func. Space., 2021 (2021), 1-9. https://doi.org/10.1155/2021/6615976 doi: 10.1155/2021/6615976
    [7] F. Uddin, K. Javed, H. Aydi, U. Ishtiaq, M. Arshad, Control fuzzy metric spaces via orthogonality with an application, J. Math., 2021 (2021), 1-12. https://doi.org/10.1155/2021/5551833 doi: 10.1155/2021/5551833
    [8] B. Schweizer, A. Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), 313-334. https://doi.org/10.2140/pjm.1960.10.313 doi: 10.2140/pjm.1960.10.313
    [9] F. Mehmood, R. Ali, N. Hussain, Contractions in fuzzy rectangular b-metric spaces with application, J. Intell. Fuzzy Syst., 37 (2019), 1275-1285. https://doi.org/10.3233/JIFS-182719 doi: 10.3233/JIFS-182719
    [10] M. A. Alghamdi, N. Hussain, P. Salimi, Fixed point and coupled fixed point theorems in b-metric-like spaces, J. Inequal. Appl., 2013 (2013), 1-25. https://doi.org/10.1186/1029-242X-2013-402 doi: 10.1186/1029-242X-2013-402
    [11] S. Shukla, M. Abbas, Fixed point results in fuzzy metric-like spaces, Iran. J. Fuzzy Syst., 11 (2014), 81-92. https://doi.org/10.22111/IJFS.2014.1724 doi: 10.22111/IJFS.2014.1724
    [12] S. Shukla, D. Gopal, A. F. Roldán-López-de-Hierro, Some fixed point theorems in 1-M-complete fuzzy metric-like spaces, Int. J. Gen. Syst., 45 (2016), 815-829. https://doi.org/10.1080/03081079.2016.1153084 doi: 10.1080/03081079.2016.1153084
    [13] H. A. Hammad, M. De La Sen, H. Aydi, Generalized dynamic process for an extended multi-valued F-contraction in metric-like spaces with applications, Alex. Eng. J., 59 (2020), 3817-3825. https://doi.org/10.1016/j.aej.2020.06.037 doi: 10.1016/j.aej.2020.06.037
    [14] A. Amini-Harandi, Metric-likes paces, partial metric spaces and fixed point, Fixed Point Theory Appl., 2012 (2012), 1-10. https://doi.org/10.1186/1687-1812-2012-204 doi: 10.1186/1687-1812-2012-204
    [15] N. Mlaiki, K. Abodayeh, H. Aydi, T. Abdeljawad, M. Abuloha, Rectangular metric-like type spaces and related fixed point, J. Math., 2018 (2018), 1-7. https://doi.org/10.1155/2018/3581768 doi: 10.1155/2018/3581768
    [16] R. Georgea, S. Radenović, K. P. Reshma, S. Shukla, Rectangular b-metric spaces and contraction principles, J. Nonlinear Sci. Appl., 8 (2015), 1005-1013. http://dx.doi.org/10.22436/jnsa.008.06.11 doi: 10.22436/jnsa.008.06.11
    [17] N. Saleem, H. Işık, S. Furqan, C. Park, Fuzzy double controlled metric spaces and related results, J. Intell. Fuzzy Syst., 40 (2021), 9977-9985. https://doi.org/10.3233/JIFS-202594 doi: 10.3233/JIFS-202594
    [18] I. Uddin, A. Perveen, H. Işık, R. Bhardwaj, A solution of Fredholm integral inclusions via Suzuki-type fuzzy contractions, Math. Probl. Eng., 2021 (2021), 1-8. https://doi.org/10.1155/2021/6579405 doi: 10.1155/2021/6579405
    [19] K. Javed, F. Uddin, H. Aydi, A. Mukheimer, M. Arshad, Ordered-theoretic fixed point results in fuzzy b-metric spaces with an application, J. Math., 2021 (2021), 1-7. https://doi.org/10.1155/2021/6663707 doi: 10.1155/2021/6663707
    [20] K. Javed, H. Aydi, F. Uddin, M. Arshad, On orthogonal partial b-metric spaces with an application, J. Math., 2021 (2021), 1-7. https://doi.org/10.1155/2021/6692063 doi: 10.1155/2021/6692063
    [21] M. U. Ali, H. Aydi, M. Alansari, New generalizations of set valued interpolative Hardy-Rogers type contractions in b-metric spaces, J. Func. Space., 2021 (2021), 1-8. https://doi.org/10.1155/2021/6641342 doi: 10.1155/2021/6641342
    [22] D. Rakić, A. Mukheimer, T. Došenović, Z. D. Mitrović, S. Radenović, Some new fixed point results in b-metric spaces, J. Inequal. Appl., 2020 (2020), 1-14. https://doi.org/10.1186/s13660-020-02371-3 doi: 10.1186/s13660-020-02371-3
    [23] D. Rakić, T. Došenović, Z. D. Mitrović, M. De La Sen, S. Radenović, Some fixed point theorems of Ćirić type in fuzzy metric spaces, Mathematics, 8 (2020), 1-15. https://doi.org/10.3390/math8020297 doi: 10.3390/math8020297
    [24] P. Debnath, N. Konwar, S. Radenović, Metric fixed point theory: Applications in science, engineering and behavioural sciences, Singapore: Spring, 2021. https://doi.org/10.1007/978-981-16-4896-0
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