Best proximity point theorems for supreme proximal contractions
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.
KeywordsBest proximity point Fixed point Proximal contraction Optimal approximate solution
Mathematics Subject Classification47H10 47H09
- 3.Karpagam, S., Agrawal, S.: Best proximity points for cyclic contractions (preprint) Google Scholar