**3. Conclusions**

In the present paper, we find a smaller upper bound and more accurate estimation for the functional |*<sup>H</sup>*2(2)| for functions in the class CΣ with *<sup>G</sup>*(*w*) = *g*<sup>−</sup><sup>1</sup>(*w*) which is an improvement of the result obtained by Guney et al. [34]. Obtaining a sharp estimate for |*<sup>H</sup>*2(2)| of the class CΣ with *<sup>G</sup>*(*w*) = *g*<sup>−</sup><sup>1</sup>(*w*) is still an open problem.

**Author Contributions:** Investigation: N.E.C., E.A.A., S.B. and A.M.

**Funding:** This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2019R1I1A3A01050861).

**Acknowledgments:** The authors would like to express their thanks to the referees for their constructive advices and comments that helped to improve this paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
