Best proximity point theorems for supreme proximal contractions
ANNALS OF FUNCTIONAL ANALYSIS(2019)
摘要
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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关键词
Best proximity point,Fixed point,Proximal contraction,Optimal approximate solution
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