@article{Shanmugam_Kumar_2013, title={FEKETE-SZEGO problem for a class of analytic functinos defined by convolution}, volume={44}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/1162}, DOI={10.5556/j.tkjm.44.2013.1162}, abstractNote={Let $g$ and $h$ be two fixed normalized analytic functions and $\phi$ be starlike with respect to $1,$ whose range is symmetric with respect to the real axis. Let $\mathcal{M}^{\alpha,\beta}_{g,h}(\phi)$ be the class of analytic functions $f(z)=z+a_2z^2+a_3z^3+\ldots$, satisfying the subordination $$\left(\frac{(f*g)(z)}{z}\right)^\alpha \left(\frac{(f*h)(z)}{z}\right)^{\beta}\prec \phi(z),$$ where $\alpha$ and $\beta$ are real numbers and are not zero simultaneously. In the present investigation, sharp upper bounds of the Fekete-Szego functional $|a_3-\mu a_2^2|$ for functions belonging to the class $\mathcal{M}^{\alpha,\beta}_{g,h}(\phi)$ are obtained and certain applications are also discussed.}, number={2}, journal={Tamkang Journal of Mathematics}, author={Shanmugam, Sivaprasad Kumar and Kumar, Virendra}, year={2013}, month={Jun.}, pages={187–195} }