<abstract xmlns="http://www.w3.org/1999/xhtml"><p>For a single valued mapping <italic>T</italic> in a <italic>G</italic>-complete <italic>G-</italic>metric space (<italic>X, d</italic>), we show that if <italic>T<sup>n</sup></italic>,for some <italic>n></italic> 1, is a contraction, then <italic>T</italic> itself is a contraction under another related <italic>G</italic>-metric <italic>d</italic>′. We establish moreover that if <italic>T</italic> is uniformly continuous, then <italic>d</italic>′ is <italic>G</italic>-complete.</p></abstract>

For a single valued mapping T in a G-complete G-metric space (X, d), we show that if Tn,for some n> 1, is a contraction, then T itself is a contraction under another related G-metric d′. We establish moreover that if T is uniformly continuous, then d′ is G-complete.

Related <italic>G</italic>-metrics and Fixed Points

Institut de Mathématiques et de Sciences Physiques (IMSP)

African Center for Advanced Studies (ACAS)

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":{"italic":"G","content":["Related","-metrics and Fixed Points"]}}

For a single valued mapping T in a G-complete G-metric space (X, d), we show that if Tn,for some n> 1, is a contraction, then T itself is a contraction under...

Related G-metrics and Fixed Points

Published Online: Dec 07, 2018

Page range: 64 - 72

Received: Jul 22, 2017

Accepted: Nov 12, 2017

DOI: https://doi.org/10.2478/awutm-2018-0005

Keywords
(related) -metrics, fixed point, contraction

© 2018 Yaé Ulrich O. Gaba, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Related G-metrics and Fixed Points

Published Online: Dec 07, 2018

Page range: 64 - 72

Received: Jul 22, 2017

Accepted: Nov 12, 2017

DOI: https://doi.org/10.2478/awutm-2018-0005

Keywords(related) -metrics, fixed point, contraction

© 2018 Yaé Ulrich O. Gaba, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
(related) -metrics, fixed point, contraction