Consider a nonself-mapping , where is a pair of nonempty subsets of a modular space . A best proximity point of is a point satisfying the condition: . 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.
"A Best Proximity Point Result in Modular Spaces with the Fatou Property." Abstr. Appl. Anal. 2013 (SI57) 1 - 4, 2013. https://doi.org/10.1155/2013/329451