  The class of O-metric spaces generalize several existing metric-types in
literature including metric spaces, b-metric spaces, and ultra metric spaces.
In this paper, we discuss the properties of the topology induced by an O-metric
and establish in the setting, fixed point theorems of contractions and
generalized contractions. The proofs of the theorems rely heavily on polygon
O-inequalities which are a natural generalization of the triangle inequality,
and the construction of which leads to the notion of O-series following a
pattern of functions.
