• Title/Summary/Keyword: probabilistic Menger space

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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 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.

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 POINT THEOREMS IN b-MENGER INNER PRODUCT SPACES

  • Rachid Oubrahim
    • Nonlinear Functional Analysis and Applications
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    • v.29 no.2
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    • pp.487-499
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    • 2024
  • The main motivation for this paper is to investigate the fixed point property for nonlinear contraction defined on b-Menger inner product spaces. First, we introduce a b-Menger inner product spaces, then the topological structure is discussed and the probabilistic Pythagorean theorem is given and established. Also we prove the existence and uniqueness of fixed point in these spaces. This result generalizes and improves many previously known results.

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 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.

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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DIFFERENTIAL EQUATIONS ON CLOSED SUBSETS OF A PROBABILISTIC NORMED SPACE

  • Kim, Jong-Kyu;Jin, Byoung-Jae
    • Journal of applied mathematics & informatics
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    • v.5 no.1
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    • pp.223-233
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    • 1998
  • This paper is concerned with the problem of existence of solutions to the initial value problem u'(t) = A(t, u(t)), u(a) = z in a probabilistic normed space where $A : [a,b)\;{\times}\;D->E$ is continuous, D is a closed subset of a probabilistic normed space E, and $z\;{\in}\;D$. With a dissipative type condition on A, we estabilish sufficient conditions for this initial value problem to have a solution.