Differential subordination and radius estimates for starlike functions associated with the Booth lemniscate

Authors

NAK EUN CHO
SUSHIL KUMAR
VIRENDRA KUMAR
V. RAVICHANDRAN

Abstract

We obtain several inclusions between the class of functions with positive real part and the class of starlike univalent functions associated with the Booth lemniscate. These results are proved by applying the well-known theory of differential subordination developed by Miller and Mocanu and these inclusions give sufficient conditions for normalized analytic functions to belong to some subclasses of Ma-Minda starlike functions. In addition, by proving an associated technical lemma, we compute various radii constants such as the radius of starlikeness, radius of convexity, radius of starlikeness associated with the lemniscate of Bernoulli, and other radius estimates for functions in the class of functions associated with the Booth lemniscate. The results obtained are sharp.

DOI

10.3906/mat-1706-49

Keywords

Starlike function, convex function, Booth lemniscate, radius estimate, differential subordination

First Page

1380

Last Page

1399

Recommended Citation

CHO, NAK EUN; KUMAR, SUSHIL; KUMAR, VIRENDRA; and RAVICHANDRAN, V. (2018) "Differential subordination and radius estimates for starlike functions associated with the Booth lemniscate," Turkish Journal of Mathematics: Vol. 42: No. 3, Article 51. https://doi.org/10.3906/mat-1706-49
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/51