**4. Conclusions**

We have introduced some new results for upper bounds of structured singular values and skewed structured singular values along with their dual characterizations. The characterization is defined in the sense that they act as an application for some duality argument in the given convex sets. The accomplished results on the dual characterization of structured and skewed structured singular values can be used to obtain the new direction for the computation of lower bounds of both of these quantities. The numerical treatment on the dual characterization of both structured and skewed structured singular values is our future work. The interested researchers may use this opportunity to carry out their research while making use of this contribution.

**Author Contributions:** Conceptualization, M.-U.R., J.A. and T.A.; methodology, M.-U.R., J.A. and T.A.; software, M.-U.R., J.A. and T.A.; validation, M.-U.R., J.A. and T.A.; formal analysis, M.-U.R., J.A., T.A., J.K. and W.S.; investigation, M.-U.R., J.A. and T.A.; resources, M.-U.R., J.A. and T.A.; data curation, M.-U.R., J.A. and T.A.; writing—original draft preparation, M.-U.R., J.A. and T.A.; writing—review and editing, M.-U.R., J.A., T.A., J.K. and W.S.; visualization, M.-U.R., J.A. and T.A.; supervision, J.A.; project administration, M.-U.R., J.A. and T.A.; funding acquisition, J.K. and J.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was financially supported by the Faculty of Science, Burapha University, Thailand (Grant no. *SC06/2564).*

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** Alzabut is thankful and grateful to Prince Sultan University and OST˙ IM Technical University for their endless support. J. Kongson would like to gratefully acknowledge Burapha University and the Center of Excellence in Mathematics (CEM), CHE, Sri Ayutthaya Rd., Bangkok, 10400, Thailand, for supporting this research.

**Conflicts of Interest:** The authors have stated that they have no competing interest.
