Best Proximity Point Results For Multivalued Cyclic Mappings On Partial Metric Spaces

Abstract

Let ∅≠Ŕ,Ś be subsets of a partial metric space (Ω,ϑ) and Ψ:Ŕ→Ś be a mapping. If Ŕ∩Ś=∅, it cannot have a solution of equation Ψς=ς for some ς∈Ŕ. Hence, it is sensible to investigate if there is a point ἣ satisfying ϑ(ἣ,Ψἣ)=ϑ(Ŕ,Ś) which is called a best proximity point. In this paper, we first introduce a concept of Hausdorff cyclic mapping pair. Then, we revise the definition of 0-boundedly compact on partial metric spaces. After that, we give some best proximity point results for these mappings. Hene, our results combine, generalize and extend many fixed point and best proximity point theorems in the literature as properly. Moreover, a comparative and illustrative example to demonstrate the effectiveness of our results has been presented.

Keywords

• Best proximity point
• Multivalued mappings
• Partial metric space

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