Abstract
In an attractive article, Rahman et al. introduced the split monotone Yosida variational inclusions (SMYVI) and estimate the approximate solution of the split monotone Yosida variational inclusions using nonexpansive property of operators. The main result of this paper has flaw and not correct in the present form. We modify the SMYVI and give the strong convergence theorem under some new assumptions. We also give a weak convergence theorem to solve modified split Yosida variational inclusion problem using properties of averaged operators with three new supporting lemmas.
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Acknowledgements
This work was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. (D-023-363-1440). The authors, therefore, gratefully acknowledge the DSR technical and financial support.
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Communicated by Baisheng Yan.
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Alansari, M., Dilshad, M. & Akram, M. Remark on the Yosida approximation iterative technique for split monotone Yosida variational inclusions. Comp. Appl. Math. 39, 203 (2020). https://doi.org/10.1007/s40314-020-01231-6
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DOI: https://doi.org/10.1007/s40314-020-01231-6
Keywords
- Split monotone Yosida variational inclusions
- Inverse strongly monotone operator
- Averaged operator
- Nonexpansive operator