Abstract
A new class of cyclic mappings, known as almost cyclic contractions, is introduced. Indeed, it is interesting to see that almost cyclic contractions are weaker than cyclic contractions. The main purpose of this article is to explore the existence of a best approximation but not a best proximity point for almost cyclic contractions. Further, it is interesting to observe that a best proximity point theorem for cyclic contractions is deduced from a best approximation theorem for almost cyclic contractions.
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The author is very much grateful to the referees for their fruitful and invaluable comments and suggestions.
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Sadiq Basha, S. Best approximation theorems for almost cyclic contractions. J. Fixed Point Theory Appl. 23, 32 (2021). https://doi.org/10.1007/s11784-021-00868-y
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DOI: https://doi.org/10.1007/s11784-021-00868-y
Keywords
- Best approximation
- best approximant
- cyclic mapping
- an almost cyclic contraction
- cyclic contraction
- best proximity point