Abstract
In this article, we introduce the notion of weak P γ -property and γ-controlled proximal contraction in the setting of b-metric spaces and prove best proximity results for such mappings. By restricting these results, we get some new results to study the existence of best proximity points and fixed points of mappings.
Highlights
AND PRELIMINARIESWe modify and generalized the concept of Weak P-property to overcome the finding of Almeida et al [1] for best proximity point results
AND PRELIMINARIESLet (X, ds) be a metric space
Whereas Almeida et al [1] showed that some best proximity point results proved by using the concept of Weak P-property can be obtained from their associated fixed point results
Summary
We modify and generalized the concept of Weak P-property to overcome the finding of Almeida et al [1] for best proximity point results. By using our generalized concept of Weak P-property almost all existing results of best proximity point could be further extended and the finding of Almeida et al [1] are not applicable. Abkar and Gbeleh [5] gave best proximity result for nonself multivalued mappings satisfying P-property. Jleli and Samet [9] gave the notion of α-proximal admissible and α-ψ-proximal contractive type mappings and proved the corresponding best proximity point theorems These notions and results have been extended to multivalued nonself mappings by Ali et al [10] and Choudhurya et al [11], independently.
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