A Best Proximity Point Result in Modular Spaces with the Fatou Property. (28th September 2013) - Jleli, Mohamed; Karapınar, Erdal; Samet, Bessem
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.