New best proximity point results for different types of nonself proximal contractions with an application (Q6558452)

The authors of this interesting paper are concerned with best proximity point problems in the sense of \textit{K. Fan} [Math. Z. 112, 234--240 (1969; Zbl 0185.39503)], \textit{S. Reich} [Math. Z. 125, 17--31 (1972; Zbl 0216.17302); J. Math. Anal. Appl. 62, 104--113 (1978; Zbl 0375.47031)], and of \textit{W. A. Kirk} et al. [Numer. Funct. Anal. Optimization 24, 851--862 (2003; Zbl 1054.47040)]. They first establish the existence of best proximity points for certain mappings of contractive type in complete metric spaces and then deduce several corollaries of their theorem. A pertinent example and an application to solving a functional equation are also presented.