Abstract
In this chapter we introduce the concept of G -metric on a set X, and we show some of its basic properties. We provide any G-metric space with a Hausdorff topology in which the notions of convergent and Cauchy sequences will be a key tool in almost all proofs. Later, we will study the close relationships between G-metrics and quasi-metrics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Apostol, T.: Mathematical Analysis. Addison-Wesley, Reading (1974)
Bourbaki, N.: Topologie générale. Herman, Paris (1961)
Mustafa, Z.: A new structure for generalized metric spaces with applications to fixed point theory. Ph.D. thesis, The University of Newcastle, Australia (2005)
Mustafa, Z., Sims, B.: A new approach to generalized metric spaces. J. Nonlinear Convex Anal. 7(2), 289–297 (2006)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Agarwal, R.P., Karapınar, E., O’Regan, D., Roldán-López-de-Hierro, A.F. (2015). G-Metric Spaces. In: Fixed Point Theory in Metric Type Spaces. Springer, Cham. https://doi.org/10.1007/978-3-319-24082-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-24082-4_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-24080-0
Online ISBN: 978-3-319-24082-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)