A best proximity point result in modular spaces with the Fatou property (Q2015372)

Summary: Consider a nonself-mapping \(T:A\to B\), where \((A,B)\) is a pair of nonempty subsets of a modular space \(X_\rho\). A best proximity point of \(T\) is a point \(z\in A\) satisfying the condition: \(\rho(z-Tz)=\mathrm{inf}\{\rho(x-y)\colon(x,y)\in A\times B\}\). 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.