A coupled best approximations theorem in normed spaces

We prove a coupled best approximations theorem in normed spaces. Also, we derive the results on coupled coincidence points and coupled fixed points, which were introduced by Lakshmikantham and Ćirić [V. Lakshmikantham, LJ. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. TMA, 70 (2009) 4341–4349].