A Comprehensive Analysis of Stability and Data Dependency for a Novel Jungck-type Iterative Algorithm

This study introduces a novel Jungck-type iterative algorithm for approximating coincidence points under specific contractive conditions. The research demonstrates the algorithm's strong convergence, stability, and data dependency through rigorous theoretical analysis and numerical experiments. Results indicate that the proposed method achieves a significantly faster convergence rate compared to existing Jungck-type iterations. These findings have practical implications in fields such as optimization, economic modeling, and coupled differential equations, where iterative techniques are vital.