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

الملخص EN

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.