Some coefficient bounds associated with transforms of bounded turning functions

N.  Vani; D. Vamshee  Krishna; D.  Shalini

doi:10.37863/umzh.v74i12.6671

N. Vani Gitam Inst. Sci., GITAM Univ., Visakhapatnam, India
D. Vamshee Krishna Gitam Sci., GITAM Univ., Visakhapatnam, India
D. Shalini Dr. B. R. Ambedkar Univ., Srikakulam, India

DOI: https://doi.org/10.37863/umzh.v74i12.6671

Keywords: holomorphic bounded turning function, upper bound, functionals connected with Hankel determinant, positive real part function.

Abstract

UDC 517.5

We present the derivation of an upper bound for the Hankel determinants of certain orders linked with the $k$th-root transform $[f(z ^k )] ^{\frac{1}{k}}$ of the holomorphic mapping $f(z)$ whose derivative has a positive real part with normalization, namely, $f(0)=0$ and $f'(0)=1.$

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