• Title, Summary, Keyword: complete metric space

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COMMON FIXED POINT THEOREM AND INVARIANT APPROXIMATION IN COMPLETE LINEAR METRIC SPACES

  • Nashine, Hemant Kumar
    • East Asian mathematical journal
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    • v.28 no.5
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    • pp.533-541
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    • 2012
  • A common fixed point result of Gregus type for subcompatible mappings defined on a complete linear metric space is obtained. The considered underlying space is generalized from Banach space to complete linear metric spaces, which include Banach space and complete metrizable locally convex spaces. Invariant approximation results have also been determined as its application.

THE COMPLETENESS OF CONVERGENT SEQUENCES SPACE OF FUZZY NUMBERS

  • Choi, Hee Chan
    • Korean Journal of Mathematics
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    • v.4 no.2
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    • pp.117-124
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    • 1996
  • In this paper we define a new fuzzy metric $\tilde{\theta}$ of fuzzy number sequences, and prove that the space of convergent sequences of fuzzy numbers is a fuzzy complete metric space in the fuzzy metric $\tilde{\theta}$.

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Some Properties on Intuitionistic Fuzzy Metric Space

  • Park, Jong-Seo;Kwun, Young-Chel;Park, Jin-Han
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.10 no.2
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    • pp.152-156
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    • 2010
  • We define some terminologies on intuitionistic fuzzy metric space and prove that the topology generated by any intuitionistic fuzzy metric space is metrizable. Also, we show that if the intuitionistic fuzzy metric space is complete, then the generated topology is completely metrizable, a Baire space, and that an intuitionistic fuzzy metric space is precompact if and only if every sequence has a Cauchy subsequence.

On the Intuitionistic Fuzzy Metric Spaces (직관적 퍼지거리공간에 관하여)

  • Park Jin Han;Saadati R,
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.157-160
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    • 2005
  • In this paper, we define precompact set in intuitionistic fuzzy metric spaces and prove that any subset of an intuitionistic fuzzy metric space is compact if and only if it is precompact and complete. Also we define topologically complete intuitionistic fuzzy metrizable spaces and prove that any $G\delta$ set in a complete intuitionistic fuzzy metric spaces is a topologically complete intuitionistic fuzzy metrizable space and vice versa.

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On Fixed Point Theorem of Weak Compatible Maps of Type(γ) in Complete Intuitionistic Fuzzy Metric Space

  • Park, Jong-Seo
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.11 no.1
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    • pp.38-43
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    • 2011
  • In this paper, we give definitions of compatible mappings of type(${\gamma}$) in intuitionistic fuzzy metric space and obtain common fixed point theorem under the conditions of weak compatible mappings of type(${\gamma}$) in complete intuitionistic fuzzy metric space. Our research generalize, extend and improve the results given by Sedghi et.al.[12].

Some Common Fixed Point Theorems using Compatible Maps in Intuitionistic Fuzzy Metric Space

  • Park, Jong-Seo
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.11 no.2
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    • pp.108-112
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    • 2011
  • Kaneko et a1.[4] etc many authors extended with multi-valued maps for the notion of compatible maps in complete metric space. Recently, O'Regan et a1.[5] presented fixed point and homotopy results for compatible single-valued maps on complete metric spaces. In this paper, we will establish some common fixed point theorems using compatible maps in intuitionistic fuzzy metric space.

Some Notes on Lp-metric Space of Fuzzy Sets

  • Kim, Yun-Kyong
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.10 no.3
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    • pp.242-246
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    • 2010
  • It is well-known that the space $E^n$ of fuzzy numbers(i.e., normal, upper-semicontinuous, compact-supported and convex fuzzy subsets)in the n-dimensional Euclidean space $R^n$ is separable but not complete with respect to the $L_p$-metric. In this paper, we introduce the space $F_p(R^n)$ that is separable and complete with respect to the $L_p$-metric. This will be accomplished by assuming p-th mean bounded condition instead of compact-supported condition and by removing convex condition.

COMMON FIXED POINT THEOREM IN FUZZY METRIC SPACE USING CONTROL FUNCTION

  • Kumar, Amit;Vats, Ramesh Kumar
    • Communications of the Korean Mathematical Society
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    • v.28 no.3
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    • pp.517-526
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    • 2013
  • We give a fixed point theorem for complete fuzzy metric space which generalizes fuzzy Banach contraction theorems established by V. Gregori and A. Spena [Fuzzy Sets and Systems 125 (2002), 245-252] using notion of altering distance, initiated by Khan et al. [Bull. Austral. Math. Soc. 30 (1984), 1-9] in metric spaces.

SOME ĆIRIC TYPE FIXED POINT RESULTS IN NON-ARCHIMEDEAN MODULAR METRIC SPACES

  • Hosseini, Hoda;Gordji, Majid Eshaghi
    • The Pure and Applied Mathematics
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    • v.26 no.4
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    • pp.215-231
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    • 2019
  • In this paper, we establish some ĆIRIC type fixed point theorems in α-complete and orbitally T-complete non-Archimedean modular metric spaces. Meanwhile, we present an illustrative example to emphasis the realized improvements. These obtained results extend and improve certain well known results in the literature.

FIXED POINT THEOREMS FOR GENERALIZED NONEXPANSIVE SET-VALUED MAPPINGS IN CONE METRIC SPACES

  • Kim, Seung-Hyun;Lee, Byung-Soo
    • East Asian mathematical journal
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    • v.27 no.5
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    • pp.557-564
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    • 2011
  • In 2007, Huang and Zhang [1] introduced a cone metric space with a cone metric generalizing the usual metric space by replacing the real numbers with Banach space ordered by the cone. They considered some fixed point theorems for contractive mappings in cone metric spaces. Since then, the fixed point theory for mappings in cone metric spaces has become a subject of interest in [1-6] and references therein. In this paper, we consider some fixed point theorems for generalized nonexpansive setvalued mappings under suitable conditions in sequentially compact cone metric spaces and complete cone metric spaces.