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Peer-reviewedCC BY 4.0Axioms

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

  • Arifuzzaman1
  • Syed Shakaib Irfan2
  • Ahmad Almutlg3
  • Iqbal Ahmad4
4 affiliations
  1. 1Department of Mathematics, Fareast International University, Dhaka 1230, Bangladesh
  2. 2Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
  3. 3Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia
  4. 4Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah 52571, Saudi Arabia
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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.

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Cite

BibTeXRIS
BibTeX
@article{arifuzzaman2026fixedpoint,
  title = {{Fixed-Point Formulation and Parallel Averaged Operator Algorithms for Generalized Variational Inclusion Problems}},
  author = {Arifuzzaman and Syed Shakaib Irfan and Ahmad Almutlg and Iqbal Ahmad},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15100758},
  url = {https://www.mdpi.com/2075-1680/15/10/758},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Fixed-Point Formulation and Parallel Averaged Operator Algorithms for Generalized Variational Inclusion Problems
AU  - Arifuzzaman
AU  - Syed Shakaib Irfan
AU  - Ahmad Almutlg
AU  - Iqbal Ahmad
PY  - 2026
DA  - 2026/10/11
JO  - Axioms
DO  - 10.3390/axioms15100758
UR  - https://www.mdpi.com/2075-1680/15/10/758
AB  - 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.
SN  - 2075-1680
ER  -