Best proximity point theorems for cyclic orbital Meir–Keeler contraction maps

We introduce a notion of cyclic orbital Meir–Keeler contraction and give sufficient conditions for the existence of fixed points and best proximity points of such a map. Our main result is a generalization of a best proximity point result due to Di Bari et al. [C. Di Bari, T. Suzuki, C. Vetro, Best proximity points for cyclic Meir–Keeler contractions, Nonlinear Anal. 69 (2008) 3790–3794].