• Title/Summary/Keyword: Probabilistic metric space

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FIXED POINT THEOREMS VIA FAMILY OF MAPS IN WEAK NON-ARCHIMEDEAN MENGER PM-SPACES

  • Singh, Deepak;Ahmed, Amin
    • The Pure and Applied Mathematics
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    • v.20 no.3
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    • pp.181-198
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    • 2013
  • C. Vetro [4] gave the concept of weak non-Archimedean in fuzzy metric space. Using the same concept for Menger PM spaces, Mishra et al. [22] proved the common fixed point theorem for six maps, Also they introduced semi-compatibility. In this paper, we generalized the theorem [22] for family of maps and proved the common fixed point theorems using the pair of semi-compatible and reciprocally continuous maps for one pair and R-weakly commuting maps for another pair in Menger WNAPM-spaces. Our results extends and generalizes several known results in metric spaces, probabilistic metric spaces and the similar spaces.

SEM-COMPATIBILITY AND FIXED POINT THEOREM IN MENGER SPACE

  • Singh, Bijendra;Jain, Shishir
    • Journal of the Chungcheong Mathematical Society
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    • v.17 no.1
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    • pp.1-17
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    • 2004
  • In this paper, the concept of semi-compatibility in Menger space is introduced and it is used to prove results on the existence of a unique common fixed point of four self-maps. These results are a very wide improvement of Mishra [8], Dedeic and Sarapa [3, 4], Cain and Kasril [1], and Sehgal and Bharucha Reid [10].

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A COMMON FIXED POINT THEOREM FOR A SEQUENCE OF MAPS IN A GENERALIZED MENGER SPACE

  • Jain, Shobha;Jain, Shishi;Bahdhur, Lal
    • East Asian mathematical journal
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    • v.24 no.4
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    • pp.359-368
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    • 2008
  • The object of this paper is to establish a unique common fixed point theorem through weak compatibility for a sequence of self-maps satisfying a generalized contractive condition in a generalized Menger space. It improves and generalizes the result of Milovanovic-Arandelovic [2], Vasuki [10] and Sehgal and Bharucha-Reid [8]. All the results presented in this paper are new.

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FIXED POINTS OF GENERALIZED KANNAN TYPE MAPPINGS IN GENERALIZED MENGER SPACES

  • Choudhury, Binayak S.;Das, Krishnapada
    • Communications of the Korean Mathematical Society
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    • v.24 no.4
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    • pp.529-537
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    • 2009
  • Generalized Menger space introduced by the present authors is a generalization of Menger space as well as a probabilistic generalization of generalized metric space introduced by Branciari [Publ. Math. Debrecen 57 (2000), no. 1-2, 31-37]. In this paper we prove a Kannan type fixed point theorem in generalized Menger spaces. We also support our result by an example.

SOME FIXED POINT THEOREMS VIA COMMON LIMIT RANGE PROPERTY IN NON-ARCHIMEDEAN MENGER PROBABILISTIC METRIC SPACES

  • Nashine, Hemant Kumar;Kadelburg, Zoran
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.3
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    • pp.789-807
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    • 2015
  • We propose coincidence and common fixed point results for a quadruple of self mappings satisfying common limit range property and weakly compatibility under generalized ${\Phi}$-contractive conditions i Non-Archimedean Menger PM-spaces. As examples we exhibit different types of situations where these conditions can be used. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.