Fixed-disc results via simulation functions

Abstract

In this paper, our aim is to obtain new fixed-disc results on metric spaces. To do this, we present a newapproach using the set of simulation functions and some known fixed-point techniques. We do not need to have somestrong conditions such as completeness or compactness of the metric space or continuity of the self-mapping in ourresults. Taking only one geometric condition, we ensure the existence of a fixed disc of a new type contractive mapping.