A Dynamical Systems Approach to Generalized Cayley Inclusion Problem and Convergence Rate Comparison of Iterative Algorithms

This paper studies a generalized Cayley inclusion problem governed by a K·,·-co-monotone mapping in a real Hilbert space. We show that the proposed inclusion problem can be equivalently reformulated as a fixed-point problem. Exploiting this equivalence, an inertial extrapolation algorithm is developed to compute solutions of the generalized Cayley inclusion problem. Several related iterative algorithms are also introduced as special cases within the proposed framework. Under suitable assumptions on the underlying mappings, strong convergence results for the sequences generated by these algorithms are established. Furthermore, we investigate the associated resolvent-based dynamical system and prove that its trajectory converges globally and exponentially to the unique solution of the inclusion problem. Numerical results are provided to demonstrate the effectiveness of the proposed methods, and a comparative analysis of convergence rates and computational efficiency is carried out using convergence plots and detailed computational tables.