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Fixed and periodic points in the probabilistic normed and metric spaces

Author

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  • Ghaemi, M.B.
  • Razani, Abdolrahman

Abstract

In this paper, a fixed point theorem is proved, i.e., if A is a C-contraction in the Menger space (S,F) and E⊂S be such that A(E)¯ is compact, then A has a fixed point. In addition, under the same condition, the existence of a periodic point of A is proved. Finally, a fixed point theorem in probabilistic normed spaces is proved.

Suggested Citation

  • Ghaemi, M.B. & Razani, Abdolrahman, 2006. "Fixed and periodic points in the probabilistic normed and metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1181-1187.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:5:p:1181-1187
    DOI: 10.1016/j.chaos.2005.08.192
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    Citations

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    Cited by:

    1. Ghaemi, M.B. & Lafuerza-Guillen, Bernardo & Razani, A., 2009. "A common fixed point for operators in probabilistic normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1361-1366.
    2. Razani, Abdolrahman & Fouladgar, Kaveh, 2007. "Extension of contractive maps in the Menger probabilistic metric space," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1724-1731.
    3. Miheţ, Dorel, 2009. "Fixed point theorems in probabilistic metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1014-1019.
    4. Miheţ, Dorel, 2009. "A note on a fixed point theorem in Menger probabilistic quasi-metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2349-2352.
    5. Ćirić, Ljubomir B. & Ješić, Siniša N. & Ume, Jeong Sheok, 2008. "The existence theorems for fixed and periodic points of nonexpansive mappings in intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 781-791.

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