Fekete–Szegö problem for some starlike functions related to shell-like curves

Year, pages: 2016, 135 - 140

In this note, we investigate the Fekete-Szegö problem for a class $\mathcal{SL}$ of functions $f$ analytic in the open unit disc $\Delta=\{z: |z|<1\}$ (and which is related to a shell-like curve associated with Fibonacci numbers) satisfying the conditions that $$ f(0)=0, f'(0)=1 and \frac{zf'(z)}{f(z)} \prec \frac{1+\tau^2z^2}{1-\tau z-\tau^2z^2} (z\in \Delta), $$ where $\prec$ denotes the subordination and the number $\tau=(1-\sqrt{5})/2$ is such that $|\tau|$ fulfils the golden section of the segment $[0,1]$.

Raina, R., Sokół, J. 2016. Fekete–Szegö problem for some starlike functions related to shell-like curves. In Mathematica Slovaca, vol. 66, no.1, pp. 135-140. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0123

Raina, R., Sokół, J. (2016). Fekete–Szegö problem for some starlike functions related to shell-like curves. Mathematica Slovaca, 66(1), 135-140. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0123