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

Authors : Mustafa ASLANTAŞ

Pages : 631-642

Doi:10.35378/gujs.815957

View : 19 | Download : 8

Publication Date : 2022-06-01

Article Type : Research Paper

Abstract :Let ∅≠Ŕ,Ś be subsets of a partial metric space insert ignore into journalissuearticles values(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 ϑinsert ignore into journalissuearticles values(ἣ,Ψἣ);=ϑinsert ignore into journalissuearticles values(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