Influence of θ-metric spaces on the diameter of rough weighted I_2-limit set

Abstract

Primarily in this article we counter an example of finite θ-metric space which is not a metric space establish by Chanda et al. (Filomat 31 (11) (2017) 3365-3375) in the year 2017 and show that this result can't be correct. In support of our demand we bring up with so many non-trivial interesting examples over infinite θ-metric spaces which is not a metric space. Also our next aim is to work with the diameter of the rough weighted I_2-limit set. We claim that the diameter grows larger than previous [5,12] over θ-metric spaces. We propose various examples and a theorem to prove the assertion.