Abstract
In this paper, we prove versions of Khan type and Dass–Gupta type contraction principles in \(b_{v}(s)\)-metric spaces. The results which we obtain generalize many known results in fixed point theory. Examples show how these results can be applied in concrete situations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ahmad, J., Arshad, M., Vetro, C.: On a theorem of Khan in a generalized metric space. Int. J. Anal. Article ID 852727, p 6 (2013)
Ansari, A.H., Aydi, H., Kumari, P.S., Yildirim, I.: New fixed point results via \(C\)-class functions in \(b\)-rectangular metric spaces. Commun. Math. Anal. 9(2), 109–126 (2018)
Aydi, H., Chen, C.M., Karapinar, E.: Interpolative Ciric-Reich-Rus type contractions via the Branciari distance. Mathematics 7(1), 84 (2019). https://doi.org/10.3390/math7010084
Aydi, H., Czerwik, S.: Fixed point theorems in generalized \(b\)-metric spaces. Modern Discrete Math. Anal. 131, 1–9 (2018)
Bakhtin, I.A.: The contraction mapping principle in quasimetric spaces. Funct. Anal. Ulianowsk Gos. Ped. Inst. 30, 26–37 (1989)
Branciari, A.: A fixed point theorem of Banach–Caccioppoli type on a class of generalized metric spaces. Publ. Math. Debr. 57, 31–37 (2000)
Czerwik, S.: Contraction mappings in b-metric spaces. Acta Math. Inform. Univ. Ostrav. 1, 5–11 (1993)
Dass, B.K., Gupta, S.: An extension of Banach contracion principle through rational expression. Indian J. Pure Appl. Math. 6, 1455–1458 (1975)
Fisher, B.: A note on a theorem of Khan. Rend. Ist. Mat. Univ. Trieste 10, 1–4 (1978)
George, R., Radenović, S., Reshma, K.P., Shukla, S.: Rectangular b-metric space and contraction principles. J. Nonlinear Sci. Appl. 8, 1005–1013 (2015)
Gulyaz, S., Karapinar, E., Erhan, I.M.: Generalized \(\alpha \)-Meir–Keeler contraction mappings on Branciari b-metric spaces. Filomat 31(17), 5445–5456 (2017)
Jaggi, D.S.: Some unique fixed point theorems. Indian J. Pure. Appl. Math. 8, 223–230 (1977)
Jovanović, M., Kadelburg, Z., Radenović, S.: Common fixed point results in metric-type spaces. Fixed Point Theory Appl. Article ID 978121, p 15 (2010)
Karapinar, E.: Some fixed points results on Branciari metric spaces via implicit functions. Carpathian J. Math. 31(3), 339–348 (2015)
Karapinar, E., Pitea, A.: On \(\alpha \)-\(\psi \)-Geraghty contraction type mappings on quasi-Branciari metric spaces. J. Nonlinear Convex Anal. 17(7), 1291–1301 (2016)
Karapınar, E., Czerwik, S., Aydi, H.: \((\alpha ,\psi )\)-Meir–Keeler contraction mappings in generalized b-metric spaces. J. Funct. Spaces. Article ID 3264620, p 4 (2018)
Khan, M.S.: A fixed point theorem for metric spaces. Rend. Inst. Math. Univ. Trieste 8, 69–72 (1976)
Mitrović, Z.D., Radenović, S.: The Banach and Reich contractions in \(b_{v}(s)\)-metric spaces. J. Fixed Point Theory Appl. 19, 3087–3095 (2017)
Mustafa, Z., Karapinar, E., Aydi, H.: A discussion on generalized almost contractions via rational expressions in partially ordered metric spaces. J. Inequal. Appl. 2014, 219 (2014)
Piri, H., Rahrovi, S., Kumam, P.: Khan type fixed point theorems in a generalized metric space. J. Math. Comput. Sci. 16, 211–217 (2016)
Roshan, J.R., Parvaneh, V., Kadelburg, Z., Hussain, N.: New fixed point results in \(b\)-rectangular metric spaces. Nonlinear Anal. Model. Control 21(5), 614–634 (2016)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Mitrović, Z.D., Aydi, H., Kadelburg, Z. et al. On some rational contractions in \(\mathbf {b_{v}(s)}\)-metric spaces. Rend. Circ. Mat. Palermo, II. Ser 69, 1193–1203 (2020). https://doi.org/10.1007/s12215-019-00465-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12215-019-00465-6