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Common fixed point theorems in intuitionistic fuzzy metric spaces and L-fuzzy metric spaces with nonlinear contractive condition

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  • Ješić, Siniša N.
  • Babačev, Nataša A.

Abstract

The purpose of this paper is to prove some common fixed point theorems for a pair of R-weakly commuting mappings defined on intuitionistic fuzzy metric spaces [Park JH. Intuitionistic fuzzy metric spaces. Chaos, Solitons & Fractals 2004;22:1039–46] and L-fuzzy metric spaces [Saadati R, Razani A, Adibi H. A common fixed point theorem in L-fuzzy metric spaces. Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2006.01.023], with nonlinear contractive condition, defined with function, first observed by Boyd and Wong [Boyd DW, Wong JSW. On nonlinear contractions. Proc Am Math Soc 1969;20:458–64]. Following Pant [Pant RP. Common fixed points of noncommuting mappings. J Math Anal Appl 1994;188:436–40] we define R-weak commutativity for a pair of mappings and then prove the main results. These results generalize some known results due to Saadati et al., and Jungck [Jungck G. Commuting maps and fixed points. Am Math Mon 1976;83:261–3]. Some examples and comments according to the preceding results are given.

Suggested Citation

  • Ješić, Siniša N. & Babačev, Nataša A., 2008. "Common fixed point theorems in intuitionistic fuzzy metric spaces and L-fuzzy metric spaces with nonlinear contractive condition," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 675-687.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:3:p:675-687
    DOI: 10.1016/j.chaos.2006.09.048
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    1. Alaca, Cihangir & Turkoglu, Duran & Yildiz, Cemil, 2006. "Fixed points in intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1073-1078.
    2. Mohamad, Abdul, 2007. "Fixed-point theorems in intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1689-1695.
    3. Razani, Abdolrahman, 2006. "Existence of fixed point for the nonexpansive mapping of intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 367-373.
    4. El Naschie, M.S., 2006. "Fuzzy Dodecahedron topology and E-infinity spacetime as a model for quantum physics," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1025-1033.
    5. Saadati, Reza & Razani, Abdolrahman & Adibi, H., 2007. "A common fixed point theorem in L-fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 358-363.
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