Abstract
In the paper, we present the basic ideas in b-metric spaces (and b-normed spaces). The main result is the Schauder fixed point principle. For the proof, we use the method presented by Dugundji and Granas in their book [4].
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
References
S. Cobzas, S. Czerwik, The completion of generalized b-metric spaces and fixed points. Fixed Point Theory 10(2), 1–21 (2009)
S. Czerwik, Contraction mappings in b-metric spaces. Acta Math. Inform. Univ. Ostraviensis 1, 5–11 (1993)
S. Czerwik, Nonlinear set-valued contraction mappings in B-metric spaces. Atti. Sem. Mat. Fis. Univ. Modena 46(2), 263–276 (1998)
J. Dugundi, A. Granas, Fixed Point Theory (Polish Scientific Publishers, Warsaw, 1982), pp. 5–209
W. Kirk, N. Shahequation-, Fixed Point Theory in Distance Spaces (Springer, Cham, 2014)
L.A. Liusternik, V.J. Sobolev, Elements of Functional Analysis (PWN, Warsaw, 1959) (in Polish)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Czerwik, S. (2021). On b-Metric Spaces and Brower and Schauder Fixed Point Principles. In: Rassias, T.M. (eds) Approximation Theory and Analytic Inequalities . Springer, Cham. https://doi.org/10.1007/978-3-030-60622-0_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-60622-0_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-60621-3
Online ISBN: 978-3-030-60622-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)