A Best Proximity Point Result in Modular Spaces with the Fatou Property. (28th September 2013)

• Record Type: Journal Article
• Authors: Jleli, Mohamed; Karapınar, Erdal; Samet, Bessem
• Other Names: Hernandez Salvador Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-09-28
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/329451
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Consider a nonself-mapping T : A → B, where ( A, B ) is a pair of nonempty subsets of a modular space X ρ . A best proximity point of T is a point z ∈ A satisfying the condition: ρ ( z − T z ) = 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.