On Fixed Point Results of Suzuki-Type Contractions on Controlled Metric Spaces with Applications

In this paper, we introduce the concept of Suzuki-type contractions on controlled metric spaces and prove a fixed point theory. This extends and generalises the already existing results of Suzuki-type contractions on <i>b</i>−metric spaces and extended <i>b</i>−metric spaces to controlled metric spaces. Some illustrative examples are presented in order to amplify our findings. It is shown that Suzuki-type contractions in the setting of controlled metric spaces provide greater generality and flexibility compared to the setting of metric spaces. We do this by constructing an example where a Suzuki-type contraction does not guarantee a fixed point in a standard metric space but does in a controlled metric space. In this setting, the control function in the controlled metric helps to stabilise iterative sequences in proving the fixed point theory and indeed in the application. Finally, our main result is applied to show the existence of a solution for the fredholm type integral equation. The results obtained in this paper contribute to the broader study of fixed point theory and its applications in mathematical analysis and applied sciences.