This paper introduces the concept of the theta cone metric, studies its various topological properties, and gives some examples of it. Furthermore, it proves some lemmas and then uses them to give further generalizations of some well-known fixed point theorems. Specifically, Theorem 2 of the paper is a generalization of Reich’s fixed point theorem.

This paper proves the existence of a unique coupled fixed point of some type of contraction mappings defined on a complete b -cone and b -theta cone metric spaces; consequently, it extends and generalizes many previous coupled fixed point theorems.