Topology of non-triangular metric spaces and related fixed point results

Abstract

Non-triangular metric spaces have been introduced by Khojasteh and Khandani in 2020. The concept of non-triangular metric spaces is fresh and therefore, requires quite some analysis on its topology. In this article, we have made an attempt to study the topology of non-triangular metric spaces by giving a natural definition of open sets in this context. The introduction of non-triangular metric spaces has shown that there is no inherent need for the triangle inequality to prove various fixed point results. Keeping this in mind, we give a fixed point result for Suzuki type Z-contractions in the context of non-triangular metric spaces by introducing a new property of maps.