Computational Analysis of Common Fixed Points in b ‐Metric Spaces With Applications to Well‐Posedness and Projectile Motion

This article establishes common fixed‐point results for a pair of self‐mappings governed by a new Suzuki‐type contraction in the setting of complete b ‐metric spaces. The proposed framework generalizes several existing contraction principles in the literature by relaxing the traditional triangle inequality and incorporating a Suzuki‐type restriction on the domain. To further support and validate the theoretical findings, graphical and computational analyses are presented through explicit examples. An iterative algorithm is also provided to demonstrate the convergence behavior of the obtained results. Moreover, the applicability of the developed theory is illustrated by proving the existence and uniqueness of solutions to certain differential equations arising in projectile motion. In addition, the well‐posedness of the common fixed‐point problem is investigated, ensuring the stability and robustness of solutions. Overall, the study expands the scope of fixed‐point theory and provides useful tools for addressing practical problems in applied mathematics and physics.