Summary: In 2012, \(\alpha\)-\(\psi\)-contractive mappings were introduced by B. Samet, C. Vetro and P. Vetro [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 4, 2154–2165 (2012; Zbl 1242.54027)]. In fact, their technique generalized some ordered fixed point results. Recently, P. Salimi, A. Latif and N. Hussain [Fixed Point Theory Appl. 2013, Article ID 151, 19 p., electronic only (2013; Zbl 1293.54036)] introduced modified \(\alpha\)-\(\psi\)-contractive mappings. First, we show that this notion is not a real generalization for the notion of \(\alpha\)-\(\psi\)-contractive mappings. Also, we provide a new notion entitled new modified \(\alpha\)-\(\phi\)-contractive mappings and show that this notion is a real generalization for some old results.