Extensions of Well-Known Fixed-Point Theorems to Quasi M-Metric Spaces With Applications

Fixed-point theory has become a frequently studied topic due to its various applications in both metric spaces and generalized metric spaces. The fact that each study leads to new research also increases the importance of studying this theory. Under this perspective, the concept of quasi M-metric spaces, which is an example of a generalized metric space, has been introduced. In this study, some fixed-point results are presented with examples and applications, and an open problem has also been left. In this work, we aim to find a solution to this open problem. To this end, fixed-point theorems of Reich type, Chatterjea type, and Guseman type have been expressed and proved on complete quasi M-metric spaces. The obtained theoretical results are supported by the provided examples. Furthermore, to enhance the significance of the paper, an application to the fixed-circle problem, which has been a topic of recent research, has been obtained with the help of activation functions.