Chinese Quarterly Journal of Mathematics ›› 2014, Vol. 29 ›› Issue (4): 602-611.doi: 10.13371/j.cnki.chin.q.j.m.2014.04.015

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Some Notes on G-cone Metric Spaces

  

  1. 1. School of Mathematics and Statistics, Hubei Normal University2. Department of Mathematics and Statistics, Hanshan Normal University
  • Received:2013-08-06 Online:2014-12-30 Published:2020-11-27
  • About author:CAO Xiao-shuang(1988-), female, native of Zhongxiang, Hubei, a postgraduate of Hubei Normal University, engages in nonlinear analysis; XU Shao-yuan(1964-), male, native of Wuhan, Hubei, a professor of Hanshan Normal University, engages in nonlinear analysis(corresponding author).
  • Supported by:
    Supported by the Natural Science Foundation of Hubei Province Education Department(Q20132505); Supported by the Ph D Start-up Fund of Hanshan Normal University of Guangdong Province(QD20110920);

Abstract: In this paper, we introduce a G metric on the G-cone metric space and then prove that a complete G-cone metric space is always a complete G metric space and verify that a contractive mapping on the G-cone metric space is a contractive mapping on the G metric space. At last, we also give a new way to obtain the unique fixed point on G-cone metric space. 

Key words: G-cone metric space, G metric, contractive mapping

CLC Number: