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

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  • 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].

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  • 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
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    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.
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    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. Kamran, Tayyab, 2008. "Common fixed points theorems for fuzzy mappings," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1378-1382.

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