Best Proximity Point Theorems via Proximal Non-self Mappings
We prove a best proximity point theorem for proximal generalized contractive type mappings in metric spaces, which is a generalization of recent best proximity point theorems and some famous fixed point theorems due to Berinde and Suzuki. We also introduce a new class of proximal non-self mappings and obtain sufficient conditions, which ensure the existence of a best proximity point. Moreover, we define algorithms and prove that they find a best proximity point for these classes of non-self mappings in the setting of metric and Banach spaces.
KeywordsBest proximity point Berinde weak proximal contraction Proximal generalized nonexpansive Approximatively compactness
Mathematics Subject Classification47H10 47H09
The author thanks the referees for their valuable suggestions.
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