In this paper, the authors obtain some best proximity point theorems for cyclic contractive mappings using the results of D. W. Boyd and J. S. W. Wong [Proc. Am. Math. Soc. 20, 458–464 (1969; Zbl 0175.44903)] and C. S. Wong [J. Math. Anal. Appl. 37, 142–150 (1972; Zbl 0224.47036)].