**4. Conclusions**

Using the concept of the principle of subordination, we have introduced a new subclass of close-to-convex functions in U, associated with the limniscate of Bernoulli. We have then derived the upper bound on *H*3 (1) for this subclass of close-to-convex functions in U, which is associated with the limniscate of Bernoulli. Our main results are stated and proved as Theorems 1–4. These general results are motivated essentially by the earlier works which are pointed out in this presentation.

**Author Contributions:** Conceptualization, Q.Z.A. and N.K.; methodology, N.K.; software, B.K.; validation, H.M.S.; formal analysis, H.M.S.; Writing—Original draft preparation, H.M.S.; Writing—Review and editing, H.M.S.; supervision, H.M.S. H.H.S. revised the article as per suggestions from Referees.

**Funding:** The third author is partially supported by UKM grant: GUP-2017-064.

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