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

Abstract

Consider a nonself-mapping T: A -> B, where (A, B) is a pair of nonempty subsets of a modular space. X-rho. A best proximity point of T is a point z is an element of A satisfying the condition: rho(z - Tz) = inf {rho(x-y) : (x,y) is an element of A x 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.