Applications of Common Fixed-Point Results in Complex-Valued Metric Spaces to Homotopy Theory

The aim of this research article is to introduce generalized rational contractions in the context of complex-valued metric spaces and to establish novel common fixed-point theorems. Our findings generalize several well-known fixed-point theorems and contribute to the advancement of fixed-point theory. A non-trivial example is provided to demonstrate the efficacy of the obtained results. Additionally, we demonstrate the practical significance of our findings through a homotopy result.