Numerical and Analytical Study of Mixed Generalized Cayley Variational Inclusions via Parallel S ‐Iterations

This article investigates the structure and analytical properties of a system of mixed generalized Cayley variational inclusion problems (CVIPs) involving logical operations in the context of positive real‐ordered Hilbert spaces. To achieve the optimal solution, a parallel Mann iteration process is introduced. Furthermore, an alteration point problem is formulated, which is proven to be equivalent to the proposed system. Subsequently, a general parallel S ‐iteration process is developed. The convergence criteria for the proposed algorithms are rigorously established, and a numerical result is constructed in MATLAB R2024b to validate the effectiveness and applicability of the proposed theoretical results.