Kyungpook Mathematical Journal

  • 제55권2호
  • /
  • Pages.449-472
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  • 2015
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Extended by Balk Metrics

  • DOVGOSHEY, OLEKSIY (Division of Applied Problems in Contemporary Analysis, Institute Mathematics of NASU, Donetsk National University) ;
  • DORDOVSKYI, DMYTRO (Institute of Applied Mathematics and Mechanics of NASU)
  • 투고 : 2013.12.21
  • 심사 : 2014.04.11
  • 발행 : 2015.06.23
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초록

Let X be a nonempty set and $\mathcal{F}$(X) be the set of nonempty finite subsets of X. The paper deals with the extended metrics ${\tau}:\mathcal{F}(X){\rightarrow}\mathbb{R}$ recently introduced by Peter Balk. Balk's metrics and their restriction to the family of sets A with ${\mid}A{\mid}{\leqslant}n$ make possible to consider "distance functions" with n variables and related them quantities. In particular, we study such type generalized diameters $diam_{{\tau}^n}$ and find conditions under which $B{\mapsto}diam_{{\tau}^n}B$ is a Balk's metric. We prove the necessary and sufficient conditions under which the restriction ${\tau}$ to the set of $A{\in}\mathcal{F}(X)$ with ${\mid}A{\mid}{\leqslant}3$ is a symmetric G-metric. An infinitesimal analog for extended by Balk metrics is constructed.

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참고문헌

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