Abstract
We have established, in the context of metric spaces, that an F-contraction restricted to appropriate neighborhood of its fixed point is an almost contraction and obtain definition of retractions on complete metric spaces. We have illustrated such an inclusion using an example studied in Wardowski (Fixed Point Theory Appl 94:1–6, 2012) and in Minak et al. (Bull Belg Math Soc Simon Stevin 22:411–422, 2015).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agarwal, R.P.: Fixed Point Theory and Applications. Cambridge University Press, Cambridge (Maria Meehan and Donal O’Regan) (2004)
Alfuraidana, M.A., Bacharb, M., Khamsi, M.A.: Almost monotone contractions on weighted graphs. J. Nonlinear Sci. Appl. 9, 5189–5195 (2016)
Andres, J.: On the multivalued Poincare operators: topological methods in nonlinear analysis. J. Juliusz Schauder Center 10, 93 (1997)
Berinde, V., Pacurar, M.: Iterative Approximation of Fixed Points of Single-Valued Almost Contractions. Elsevier Inc, New York (2016)
Djebali, Smail: Lech Gorniewicz and Abdelghani Ouahab Solution Sets for Differential Equations and Inclusions. Walter de Gruyter GmbH, Berlin/Boston (2013)
Gorniewicz, L.: Topological Fixed Point Theory of Multivalued Mappings. Springer, Dordrecht (2006)
Minak, G., Altun, I., Romaguera, S.: Recent developments about multivalued weakly Picard operators. Bull. Belg. Math. Soc. Simon Stevin 22, 411–422 (2015)
Rus, I.A., Petruşel, A., Petruşel, G.: Fixed Point Theory: 1950–2000. Romanian Contribution. House of the Book of Science, Cluj-Napoca (2002)
Wardowski, D.: Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl. 94, 1–6 (2012)
Udo-utun, X.: On inclusion of \(F\)-contractions in \((\delta , k)\)-weak contractions. Fixed Point Theory Appl. 65, 1–6 (2014)
Udo-utun, X.A., Siddiqui, Z.U., Balla, M.Y.: An extension of the contraction mapping principle. Fixed Point Theory Apl. (Springer-Open) 2015, 162 (2015)
Acknowledgements
The author wishes to convey gratitude to the reviewers and the Editor-in-Chief for comments which have made the paper gain much more clarity.
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
Udo-utun, X.A. On retraction problem concerning inclusion of F-contractions in almost contractions. Afr. Mat. 30, 643–650 (2019). https://doi.org/10.1007/s13370-019-00672-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13370-019-00672-5