A Best Proximity Point Result in Modular Spaces with the Fatou Property

Mohamed Jleli, Erdal Karapınar and Bessem Samet

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: Consider a nonself‐mapping T : A → B, where (A, B) is a pair of nonempty subsets of a modular space Xρ. A best proximity point of T is a point z ∈ A satisfying the condition: ρ(z − Tz) = inf{ρ(x − y) : (x, y) ∈ A × B}. In this paper, we introduce the class of proximal quasicontraction nonself‐mappings in modular spaces with the Fatou property. For such mappings, we provide sufficient conditions assuring the existence and uniqueness of best proximity points.

Date: 2013
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https://doi.org/10.1155/2013/329451

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:329451

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