Some Notes on G-cone Metric Spaces

CAO Xiao-shuang, XU Shao-yuan

doi:10.13371/j.cnki.chin.q.j.m.2014.04.015

Chinese Quarterly Journal of Mathematics >

2014 , Vol. 29 >Issue 4: 602 - 611

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.04.015

Some Notes on G-cone Metric Spaces

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1. School of Mathematics and Statistics, Hubei Normal University2. Department of Mathematics and Statistics, Hanshan Normal University

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).

Received date: 2013-08-06

Online published: 2020-11-27

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）；

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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

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CAO Xiao-shuang, XU Shao-yuan . Some Notes on G-cone Metric Spaces[J]. Chinese Quarterly Journal of Mathematics, 2014 , 29(4) : 602 -611 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.04.015

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