Abstract
This article presents some best proximity point theorems for new classes of non-self mappings, called supreme proximal contractions and supreme proximal cyclic contractions, which are brought forth to generalize the notion of self-contraction. Eventually, these results explore the existence of best proximity points that serve as optimal approximate solutions to the fixed point equations of the form \(Tx=x\), where T is a supreme proximal contraction or a supreme proximal cyclic contraction. Further, it is interesting to observe that such results generalize the most celebrated and elegant Banach’s contraction to the case of non-self mappings.
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Communicated by Constantin P. Niculescu.
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Basha, S.S. Best proximity point theorems for supreme proximal contractions. Ann. Funct. Anal. 11, 87–100 (2020). https://doi.org/10.1007/s43034-019-00019-y
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DOI: https://doi.org/10.1007/s43034-019-00019-y