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.
Citation: Arifuzzaman, Syed Shakaib Irfan, Iqbal Ahmad. Iterative approaches to Yosida variational inclusion problem involving averaged operator and logical operations[J]. AIMS Mathematics, 2025, 10(12): 30696-30717. doi: 10.3934/math.20251347
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.
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Arifuzzaman, Syed Shakaib Irfan, Iqbal Ahmad. Iterative approaches to Yosida variational inclusion problem involving averaged operator and logical operations[J]. AIMS Mathematics, 2025, 10(12): 30696-30717. doi: 10.3934/math.20251347
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