Work

Fixed-Point Formulation and Parallel Averaged Operator Algorithms for Generalized Variational Inclusion Problems

Year: 2026

Type: article

Abstract: In this paper, we study a variational inclusion problem in a real ordered Hilbert space via an averaged-operator-based approach. The proposed framework combines Yosida and Cayley approximation operators with the logical XOR and XNOR operations, resulting in a unified iterative procedure for obtaining solutions. Using the relevant properties of averaged operators and the associated Yosida and Cayley operators, we derive conditions that guarantee the existence of solutions and the convergence of the resulting iterative process. The performance of the proposed schemes is further assessed against several existing iterative methods in terms of convergence characteristics and computational cost. Finally, we present numerical results obtained by MATLAB to corroborate the theoretical analysis and to demonstrate the effectiveness of the proposed methodology.

Source: Axioms

DOI: 10.3390/axioms15100758

Authors: Arifuzzaman, Syed Shakaib Irfan, Ahmad Almutlg, Iqbal Ahmad

Institutions: Aligarh Muslim University, Qassim University

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Qassim University