Iterative approaches to Yosida variational inclusion problem involving averaged operator and logical operations

This paper investigated a Yosida variational inclusion problem (YVIP) in a real ordered Hilbert space, where logical operations are incorporated through an averaged-operator framework. By reformulating the YVIP and its associated resolvent equation as equivalent fixed-point problems, we designed an iterative scheme that systematically integrates these logical and averaged-operator components. Furthermore, we analyzed the convergence of the proposed algorithms. A comparative study with existing algorithms, supported by numerical experiments, demonstrated the improved computational behavior of the proposed method. To illustrate its practical relevance, a representative MATLAB-based numerical result was also presented.