• Title/Summary/Keyword: Probabilistic metric space

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SOME COMMON FIXED POINT THEOREMS WITH CONVERSE COMMUTING MAPPINGS IN BICOMPLEX-VALUED PROBABILISTIC METRIC SPACE

  • Sarmila Bhattacharyya;Tanmay Biswas;Chinmay Biswas
    • The Pure and Applied Mathematics
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    • v.31 no.3
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    • pp.299-310
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    • 2024
  • The probabilistic metric space as one of the important generalizations of metric space, was introduced by Menger [16] in 1942. Later, Choi et al. [6] initiated the notion of bicomplex-valued metric spaces (bi-CVMS). Recently, Bhattacharyya et al. [3] linked the concept of bicomplex-valued metric spaces and menger spaces, and initiated menger space with bicomplex-valued metric. Here, in this paper, we have taken probabilistic metric space with bicomplex-valued metric, i.e., bicomplexvalued probabilistic metric space and proved some common fixed point theorems using converse commuting mappings in this space.

THE EXTENSION OF FIXED POINT THEOREMS FOR SET VALUED MAPPING

  • Shi, Yimin;Ren, Limei;Wang, Xuyan
    • Journal of applied mathematics & informatics
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    • v.13 no.1_2
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    • pp.277-286
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    • 2003
  • In this paper, the Monger Probabilistic n-metric space is presented, some Hex point theorem for set valued mapping are extended to Monger probabilistic n-metric space.

SOME RESULTS ON COMMON BEST PROXIMITY POINT AND COMMON FIXED POINT THEOREM IN PROBABILISTIC MENGER SPACE

  • Shayanpour, Hamid
    • Journal of the Korean Mathematical Society
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    • v.53 no.5
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    • pp.1037-1056
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    • 2016
  • In this paper, we define the concepts of commute proximally, dominate proximally, weakly dominate proximally, proximal generalized ${\varphi}$-contraction and common best proximity point in probabilistic Menger space. We prove some common best proximity point and common fixed point theorems for dominate proximally and weakly dominate proximally mappings in probabilistic Menger space under certain conditions. Finally we show that proximal generalized ${\varphi}$-contractions have best proximity point in probabilistic Menger space. Our results generalize many known results in metric space.

Fixed Point Theorems for Expansion Mappings on Probabilistic Metric Spaces

  • Pant, B.O.;Dimri, R.C.;Singh, S.L.
    • Honam Mathematical Journal
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    • v.9 no.1
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    • pp.77-81
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    • 1987
  • In this paper we introduce the notion of expansion mapping on a probabilistic metric space and prove common fixed point theorems for a pair of such mappings. These results being new of their kind. are interesting generafizations of some of the known results.

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Common Fixed Point Theorems in Probabllistic Metric Spaces and Extension to Uniform Spaces

  • Singh, S.L.;Pant, B.D.
    • Honam Mathematical Journal
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    • v.6 no.1
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    • pp.1-12
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    • 1984
  • Let(X, $\Im$) be a probabilistic metric space with a t-norm. Common fixed point theorems and convergence theorems generalizing the results of Ćirić, Fisher, Sehgal, Istrătescu-Săcuiu and others are proved for three mappings P,S,T on X satisfying $F_{Pu, Pv}(qx){\geq}min\left{F_{Su,Tv}(x),F_{Pu,Su}(x),F_{Pv,Tv}(x),F_{Pu,Tv}(2x),F_{Pv,Su}(2x)\right}$ for every $u, v {\in}X$, all x>0 and some $q{\in}(0, 1)$. One of the main results is extended to uniform spaces. Mathematics Subject Classification (1980): 54H25.

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WEAK COMPATIBLE MAPPINGS OF TYPE (A) AND COMMON FIXED POINTS IN MENGER SPACES

  • Pathak, H.K.;Kang, S.M.;Baek, J.H.
    • Communications of the Korean Mathematical Society
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    • v.10 no.1
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    • pp.67-83
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    • 1995
  • The notion of probabilistic metric spaces (or statistical metric spaces) was introduced and studied by Menger [19] which is a generalization of metric space, and the study of these spaces was expanede rapidly with the pioneering works of Schweizer-Sklar [25]-[26]. The theory of probabilistic metric spaces is of fundamental importance in probabilistic function analysis. For the detailed discussions of these spaces and their applications, we refer to [9], [10], [28], [30]-[32], [36] and [39].

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Fixed point theorems for fuzzy mappings and applications

  • Lee, Byung-Soo;Cho, Yeol-Je;Jung, Jong-Soo
    • Communications of the Korean Mathematical Society
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    • v.11 no.1
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    • pp.89-108
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    • 1996
  • In this paper we obtain common fixed point theorems for sequences of fuzzy mappings on Menger probabilistic metric spaces, including common fixed point theorems for sequences of multi-valued mappings, which generalize and improve some results of Lee et al. [8] and Chang [2].

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Some minimization theorems in generating spaces of quasi-metric family and applications

  • Jung, Jong-Soo;Lee, Byung-Soo;Cho, Yeol-Je
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.565-585
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    • 1996
  • In 1976, Caristi [1] established a celebrated fixed point theorem in complete metric spaces, which is a very useful tool in the theory of nonlinear analysis. Since then, several generalizations of the theorem were given by a number of authors: for instances, generalizations for single-valued mappings were given by Downing and Kirk [4], Park [11] and Siegel [13], and the multi-valued versions of the theorem were obtained by Chang and Luo [3], and Mizoguchi and Takahashi [10].

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