Afrika Matematika

, Volume 30, Issue 3–4, pp 643–650 | Cite as

On retraction problem concerning inclusion of F-contractions in almost contractions

  • Xavier Alexius Udo-utunEmail author


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).


Almost contraction F-contraction Inclusion Picard operators Weakly Picard operators 

Mathematics Subject Classification

47H09 47H10 54H25 



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.


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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of UyoUyoNigeria

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