• Title/Summary/Keyword: $D^*$-metric space

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ON FUZZY METRIC SPACE

  • Choi, J. Y.;Park, B.I.;Park, C.H.;Moon, J.R.
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 1997.10a
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    • pp.69-72
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    • 1997
  • In this papaers, we generalize the usual fuzzy metric on R, the set of all real numbers, and induce the fuzzy metric space(X, d) from a metric space(X, d)

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COMMON FIXED POINTS OF WEAK-COMPATIBLE MAPS ON D-METRIC SPACE

  • Singh, Bijendra;Jain, Shobha
    • Journal of the Chungcheong Mathematical Society
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    • v.17 no.2
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    • pp.111-124
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    • 2004
  • In [4], Dhage proved a result for common fixed point of two self-maps satisfying a contractive condition in D-metric spaces. This note proves a fixed point theorem for five self-maps under weak-compatibility in D-metric space which improves and generalizes the above mentioned result.

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SOME RATIONAL F-CONTRACTIONS IN b-METRIC SPACES AND FIXED POINTS

  • Stephen, Thounaojam;Rohen, Yumnam;Singh, M. Kuber;Devi, Konthoujam Sangita
    • Nonlinear Functional Analysis and Applications
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    • v.27 no.2
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    • pp.309-322
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    • 2022
  • In this paper, we introduce the notion of a new generalized type of rational F-contraction mapping. Further, the concept is used to obtain fixed points in a complete b-metric space. We also prove another unique fixed point theorem in the context of b-metric space. Our results are verified with example.

ON FARTHEST POINTS IN METRIC SPACES

  • Narang, T.D.
    • The Pure and Applied Mathematics
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    • v.9 no.1
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    • pp.1-7
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    • 2002
  • For A bounded subset G of a metric Space (X,d) and $\chi \in X$, let $f_{G}$ be the real-valued function on X defined by $f_{G}$($\chi$)=sup{$d (\chi, g)\in:G$}, and $F(G,\chi)$={$z \in X:sup_{g \in G}d(g,z)=sup_{g \in G}d(g,\chi)+d(\chi,z)$}. In this paper we discuss some properties of the map $f_G$ and of the set $ F(G, \chi)$ in convex metric spaces. A sufficient condition for an element of a convex metric space X to lie in $ F(G, \chi)$ is also given in this pope.

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FIXED POINT THEOREMS FOR SIX WEAKLY COMPATIBLE MAPPINGS IN $D^*$-METRIC SPACES

  • Sedghi, Shaban;Khan, M. S.;Shobe, Nabi
    • Journal of applied mathematics & informatics
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    • v.27 no.1_2
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    • pp.351-363
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    • 2009
  • In this paper, we give some new definitions of $D^*$-metric spaces and we prove a common fixed point theorem for six mappings under the condition of weakly compatible mappings in complete $D^*$-metric spaces. We get some improved versions of several fixed point theorems in complete $D^*$-metric spaces.

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COMMON FIXED POINT THEOREMS FOR A CLASS OF WEAKLY COMPATIBLE MAPPINGS IN D-METRIC SPACES

  • Kim, Jong-Kyu;Sedghi, Shaban;Shobe, Nabi
    • East Asian mathematical journal
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    • v.25 no.1
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    • pp.107-117
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    • 2009
  • In this paper, we give some new definitions of D-metric spaces and we prove a common fixed point theorem for a class of mappings under the condition of weakly compatible mappings in complete D-metric spaces. We get some improved versions of several fixed point theorems in complete D-metric spaces.

QUASI-ISOMETRIC AND WEAKLY QUASISYMMETRIC MAPS BETWEEN LOCALLY COMPACT NON-COMPLETE METRIC SPACES

  • Wang, Xiantao;Zhou, Qingshan
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.3
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    • pp.967-970
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    • 2018
  • The aim of this paper is to show that there exists a weakly quasisymmetric homeomorphism $f:(X,d){\rightarrow}(Y,d^{\prime})$ between two locally compact non-complete metric spaces such that $f:(X,d_h){\rightarrow}(Y,d^{\prime}_h)$ is not quasi-isometric, where dh denotes the Gromov hyperbolic metric with respect to the metric d introduced by Ibragimov in 2011. This result shows that the answer to the related question asked by Ibragimov in 2013 is negative.

DISCUSSION ON b-METRIC SPACES AND RELATED RESULTS IN METRIC AND G-METRIC SPACES

  • Bataihah, Anwar;Qawasmeh, Tariq;Shatnawi, Mutaz
    • Nonlinear Functional Analysis and Applications
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    • v.27 no.2
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    • pp.233-247
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    • 2022
  • In the present manuscript, we employ the concepts of Θ-map and Φ-map to define a strong (𝜃, 𝜙)s-contraction of a map f in a b-metric space (M, db). Then we prove and derive many fixed point theorems as well as we provide an example to support our main result. Moreover, we utilize our results to obtain many results in the settings of metric and G-metric spaces. Our results improve and modify many results in the literature.