Title: $η$-metric structures,
Abstract: In this paper, we discuss recent results about generalized metric spaces and
fixed point theory. We introduce the notion of $\eta$-cone metric spaces, give
some topological properties and prove some fixed point theorems for contractive
type maps on these spaces. In particular we show that theses $\eta$-cone metric
spaces are natural generalizations of both cone metric spaces and metric type
spaces.