On retraction problem concerning inclusion of F-contractions in almost contractions
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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).
KeywordsAlmost contraction F-contraction Inclusion Picard operators Weakly Picard operators
Mathematics Subject Classification47H09 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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