Abstract
In this paper, we prove new fixed-point theorems using the set of simulation functions on an S-metric space with some illustrative examples. Our results are stronger than some known fixed-point results. Furthermore, we give an application to the fixed-circle problem with respect to a simulation function.
Highlights
Showing the existence and uniqueness of a fixed point has many applications, in different fields, such as computer sciences, engineering, etc.; see [1]
Using the technique of iterations to prove the existence and uniqueness of a fixed point for a self-mapping on a metric space was first introduced by Banach in [2]
Most of the work after was basically a generalization of the work of Banach. These generalizations include more general metric spaces, or more general contractions, etc., which are important due to the fact that the more general the metric space, the larger the class, which implies that the obtained results can be applied in more different fields to solve unsolved problems
Summary
Showing the existence and uniqueness of a fixed point has many applications, in different fields, such as computer sciences, engineering, etc.; see [1]. Most of the work after was basically a generalization of the work of Banach These generalizations include more general metric spaces, or more general contractions, etc. (see [3,4]), which are important due to the fact that the more general the metric space, the larger the class, which implies that the obtained results can be applied in more different fields to solve unsolved problems. These generalizations do not just include metric spaces; they include contractions, as well. We provide the reader with a background about this space along with some lemmas
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