IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v34y2007i2p538-543.html

Common fixed point theorems for fuzzy mappings in metric space under ϕ-contraction condition

Author

Listed:
  • Abu-Donia, H.M.

Abstract

Some common fixed point theorems for multi-valued mappings under ϕ-contraction condition have been studied by Rashwan [Rashwan RA, Ahmed MA. Fixed points for ϕ-contraction type multivalued mappings. J Indian Acad Math 1995;17(2):194–204]. Butnariu [Butnariu D. Fixed point for fuzzy mapping. Fuzzy Sets Syst 1982;7:191–207] and Helipern [Hilpern S. Fuzzy mapping and fixed point theorem. J Math Anal Appl 1981;83:566–9] also, discussed some fixed point theorems for fuzzy mappings in the category of metric spaces. In this paper, we discussed some common fixed point theorems for fuzzy mappings in metric space under ϕ-contraction condition. Our investigation are related to the fuzzy form of Hausdorff metric which is a basic tool for computing Hausdorff dimensions. These dimensions help in understanding ε∞-space [El-Naschie MS. On the unification of the fundamental forces and complex time in the ε∞-space. Chaos, Solitons & Fractals 2000;11:1149–62] and are used in high energy physics [El-Naschie MS. Wild topology hyperbolic geometry and fusion algebra of high energy particle physics. Chaos, Solitons & Fractals 2002;13:1935–45].

Suggested Citation

  • Abu-Donia, H.M., 2007. "Common fixed point theorems for fuzzy mappings in metric space under ϕ-contraction condition," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 538-543.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:2:p:538-543
    DOI: 10.1016/j.chaos.2005.03.055
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906002670
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.03.055?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. El Naschie, M.S., 2005. "From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 969-977.
    2. Gerald Jungck, 1986. "Compatible mappings and common fixed points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-9, January.
    3. El Naschie, M.S., 2005. "Non-Euclidean spacetime structure and the two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 1-6.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hsien-Chung Wu, 2018. "Near Fixed Point Theorems in the Space of Fuzzy Numbers," Mathematics, MDPI, vol. 6(7), pages 1-27, June.
    2. Qiu, Dong & Shu, Lan & Guan, Jian, 2009. "Common fixed point theorems for fuzzy mappings under Φ-contraction condition," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 360-367.
    3. Azam, Akbar & Arshad, Muhammad & Beg, Ismat, 2009. "Fixed points of fuzzy contractive and fuzzy locally contractive maps," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2836-2841.
    4. Weiquan Zhang & Dong Qiu & Zhifeng Li & Gangqiang Xiong, 2012. "Common Fixed Point Theorems in a New Fuzzy Metric Space," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    5. Kamran, Tayyab, 2008. "Common fixed points theorems for fuzzy mappings," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1378-1382.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Deshpande, Bhavana, 2009. "Fixed point and (DS)-weak commutativity condition in intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2722-2728.
    2. El Naschie, M.S., 2006. "Hilbert space, the number of Higgs particles and the quantum two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 9-13.
    3. El Naschie, Mohamed Saladin, 2006. "The idealized quantum two-slit gedanken experiment revisited—Criticism and reinterpretation," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 843-849.
    4. Iovane, G., 2006. "Cantorian spacetime and Hilbert space: Part I—Foundations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 857-878.
    5. El Naschie, M.S., 2006. "Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 39-42.
    6. Budi Nurwahyu, 2019. "Common Fixed Point Theorems on Generalized Ratio Contraction Mapping in Extended Rectangular b -Metric Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2019, pages 1-14, December.
    7. Azab Abd-Allah, M. & El-Saady, Kamal & Ghareeb, A., 2009. "Rough intuitionistic fuzzy subgroup," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2145-2153.
    8. Mohammad Ali Alghamdi & Stojan Radenović & Naseer Shahzad, 2012. "On Some Generalizations of Commuting Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    9. A. Razani & V. Parvaneh, 2012. "On Generalized Weakly G‐Contractive Mappings in Partially Ordered G‐Metric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    10. Yang, Ciann-Dong, 2007. "The origin and proof of quantization axiom p→pˆ=-iℏ∇ in complex spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 274-283.
    11. Khastan, A. & Ivaz, K., 2009. "Numerical solution of fuzzy differential equations by Nyström method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 859-868.
    12. Vishal Gupta & Nitika Garg & Rahul Shukla, 2025. "Some Novel Fixed‐Point Results in Neutrosophic Soft Metric Space With Application in Decision‐Making to Select the Optimal Adsorbent," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    13. Falcón, Sergio & Plaza, Ángel, 2009. "The metallic ratios as limits of complex valued transformations," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 1-13.
    14. Chi-Ming Chen, 2012. "Common Fixed‐Point Theorems in Complete Generalized Metric Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    15. Rqeeb Gubran & Mohammad Imdad, 2016. "Results on Coincidence and Common Fixed Points for (ψ,φ) g -Generalized Weakly Contractive Mappings in Ordered Metric Spaces," Mathematics, MDPI, vol. 4(4), pages 1-13, December.
    16. El Naschie, M.S., 2006. "Elementary prerequisites for E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 579-605.
    17. Cho, Yeol Je & Sedghi, Shaban & Shobe, Nabi, 2009. "Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2233-2244.
    18. Sumit Chandok & Simona Dinu, 2013. "Common Fixed Points for Weak ψ‐Contractive Mappings in Ordered Metric Spaces with Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    19. J. R. Morales & E. M. Rojas, 2012. "Some Generalizations of Jungck's Fixed Point Theorem," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-19, November.
    20. Lucas Wangwe & Santosh Kumar, 2022. "Common Fixed Point Theorems for F‐Kannan–Suzuki Type Mappings in TVS‐Valued Cone Metric Space with Some Applications," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:34:y:2007:i:2:p:538-543. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.