ON A STUDY OF BEST PROXIMITY POINTS FOR R-PROXIMAL CONTRACTIONS IN GAUGE SPACES

In this paper, we prove the existence and uniqueness of best proximity points for non-self mappings satisfying the R-proximal contraction condition of the first or the second kind, in the setting of complete gauge spaces. The class of R-functions is a consistent one, and includes many other important classes, such as simulation functions or manageable functions. Moreover, a direct connection could be established between the classes of Geraghty functions and R-functions, respectively. Based on these connections, some classical best proximity points outcomes are recovered as corollaries.