Discussion on generalized-\((\alpha\psi,\beta\phi)\)-contractive mappings via generalized altering distance function and related fixed point theorems (Q1722477)

Summary: We extend the notion of \((\alpha\psi,\beta\phi)\)-\textit{contractive mapping}, a very recent concept by the first two authors [Fixed Point Theory Appl. 2013, Paper No. 205, 18 p. (2013; Zbl 1469.54063)]. This allows us to consider contractive conditions that generalize a wide range of nonexpansive mappings in the setting of metric spaces provided with binary relations that are not necessarily neither partial orders nor preorders. Thus, using this kind of contractive mappings, we show some related fixed point theorems that improve some well-known recent results and can be applied in a variety of contexts.