ON MODIFIED α-φ-CONTRACTIONS

In 2012, α-ψ-contractive mappings were introduced by Samet, Vetro and Vetro [Nonlinear Anal., 75(2012), 2154-2165.]. In fact, their technique generalized some ordered fixed point results. Recently, Salimi, Latif and Hussain introduced modified α- ψ-contractive mappings [Fixed Point Theory Appl., (2013), 2013:151]. First, we show that this notion is not a real generalization for the notion of α-ψ-contractive mappings. Also, we provide a new notion entitled new modified α-φ-contractive mappings and show that this notion is a real generalization for some old results.