Fixed point theorems for (ξ,α)-expansive mappings in complete metric spaces

In this paper, we introduce a new, simple and unified approach to the theory of expansive mappings. We present a new category of expansive mappings called (ξ,α)-expansive mappings and study various fixed point theorems for such mappings in complete metric spaces. Further, we shall use these theorems to derive coupled fixed point theorems in complete metric spaces. Our new notion complements the concept of α-ψ-contractive type mappings introduced recently by Samet et al. (Nonlinear Anal. 2011, doi:10.1016/j.na.2011.10.014). The presented theorems extend, generalize and improve many existing results in the literature. Some comparative examples are constructed which illustrate our results in comparison to some of the existing ones in literature.